TSTP Solution File: LCL707^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:26:13 EDT 2024
% Result : Theorem 0.78s 1.01s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 27 22:00:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.51 %----Proving TH0
% 0.78/1.01 --- Run --ho-elim --full-saturate-quant at 10...
% 0.78/1.01 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.jICiHzm6Hm/cvc5---1.0.5_15428.smt2
% 0.78/1.01 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.jICiHzm6Hm/cvc5---1.0.5_15428.smt2
% 0.78/1.01 (assume a0 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.78/1.01 (assume a1 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.78/1.01 (assume a2 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.78/1.01 (assume a3 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.78/1.01 (assume a4 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.78/1.01 (assume a5 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.78/1.01 (assume a6 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.78/1.01 (assume a7 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.78/1.01 (assume a8 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.78/1.01 (assume a9 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.78/1.01 (assume a10 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.78/1.01 (assume a11 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.78/1.01 (assume a12 (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.78/1.01 (assume a13 (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.78/1.01 (assume a14 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.78/1.01 (assume a15 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.78/1.01 (assume a16 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.78/1.01 (assume a17 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.78/1.01 (assume a18 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.78/1.01 (assume a19 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.78/1.01 (assume a20 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U))))))
% 0.78/1.01 (assume a21 (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U))))))
% 0.78/1.01 (assume a22 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U))))))
% 0.78/1.01 (assume a23 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.78/1.01 (assume a24 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.78/1.01 (assume a25 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T)))))))
% 0.78/1.01 (assume a26 (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))))))))
% 0.78/1.01 (assume a27 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.78/1.01 (assume a28 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.78/1.01 (assume a29 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.78/1.01 (assume a30 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.78/1.01 (assume a31 (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ tptp.mweakly_connected R) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))))
% 0.78/1.01 (assume a32 true)
% 0.78/1.01 (step t1 (cl (not (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) false)) (not (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) false) :rule equiv_pos2)
% 0.78/1.01 (anchor :step t2 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t2 (cl (and (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))) (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))) (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))) (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))) (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))) (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))))) (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U))))) (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U))))) (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U))))) (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T))))))) (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S))))) (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) (not (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) (not (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W)))))) (not (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) (not (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))))))) (not (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) (not (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))))))) (not (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))))) (not (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U)))))) (not (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U)))))) (not (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U)))))) (not (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T)))))))) (not (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S)))))) (not (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S))))) (not (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V)))))))) (not (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t3 (cl (not (= (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))) (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))))) (not (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t4 (cl (= tptp.mcountersatisfiable tptp.mcountersatisfiable)) :rule refl)
% 0.78/1.01 (anchor :step t2.t5 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi)))
% 0.78/1.01 (step t2.t5.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t5.t2 (cl (= (exists ((W $$unsorted)) (not (@ Phi W))) (not (forall ((W $$unsorted)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule bind)
% 0.78/1.01 (step t2.t6 (cl (= (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))) (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))))) :rule cong :premises (t2.t4 t2.t5))
% 0.78/1.01 (step t2.t7 (cl (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule resolution :premises (t2.t3 t2.t6 a30))
% 0.78/1.01 (step t2.t8 (cl (not (= (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))) (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))))) (not (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W))))) (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t9 (cl (= tptp.msatisfiable tptp.msatisfiable)) :rule refl)
% 0.78/1.01 (anchor :step t2.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi)))
% 0.78/1.01 (step t2.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t10.t2 (cl (= (exists ((W $$unsorted)) (@ Phi W)) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule bind)
% 0.78/1.01 (step t2.t11 (cl (= (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))) (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))))) :rule cong :premises (t2.t9 t2.t10))
% 0.78/1.01 (step t2.t12 (cl (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule resolution :premises (t2.t8 t2.t11 a29))
% 0.78/1.01 (step t2.t13 (cl (not (= (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))))))) (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))))) (not (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))) (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t14 (cl (= tptp.mweakly_directed tptp.mweakly_directed)) :rule refl)
% 0.78/1.01 (anchor :step t2.t15 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t15.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (anchor :step t2.t15.t2 :args ((S $$unsorted) (:= S S) (T $$unsorted) (:= T T) (U $$unsorted) (:= U U)))
% 0.78/1.01 (step t2.t15.t2.t1 (cl (= S S)) :rule refl)
% 0.78/1.01 (step t2.t15.t2.t2 (cl (= T T)) :rule refl)
% 0.78/1.01 (step t2.t15.t2.t3 (cl (= U U)) :rule refl)
% 0.78/1.01 (step t2.t15.t2.t4 (cl (= (and (@ (@ R S) T) (@ (@ R S) U)) (and (@ (@ R S) T) (@ (@ R S) U)))) :rule refl)
% 0.78/1.01 (step t2.t15.t2.t5 (cl (= (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))) (not (forall ((V $$unsorted)) (not (and (@ (@ R T) V) (@ (@ R U) V))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t15.t2.t6 (cl (= (forall ((V $$unsorted)) (not (and (@ (@ R T) V) (@ (@ R U) V)))) (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t15.t2.t7 (cl (= (not (forall ((V $$unsorted)) (not (and (@ (@ R T) V) (@ (@ R U) V))))) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))) :rule cong :premises (t2.t15.t2.t6))
% 0.78/1.01 (step t2.t15.t2.t8 (cl (= (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))) :rule trans :premises (t2.t15.t2.t5 t2.t15.t2.t7))
% 0.78/1.01 (step t2.t15.t2.t9 (cl (= (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))))) :rule cong :premises (t2.t15.t2.t4 t2.t15.t2.t8))
% 0.78/1.01 (step t2.t15.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))) :rule bind)
% 0.78/1.01 (step t2.t15.t3 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t15.t4 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))) :rule trans :premises (t2.t15.t2 t2.t15.t3))
% 0.78/1.01 (step t2.t15 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))))))) :rule bind)
% 0.78/1.01 (step t2.t16 (cl (= (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V))))))) (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))))) :rule cong :premises (t2.t14 t2.t15))
% 0.78/1.01 (step t2.t17 (cl (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V)))))))))) :rule resolution :premises (t2.t13 t2.t16 a26))
% 0.78/1.01 (step t2.t18 (cl (not (= (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))))) (not (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))) (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t19 (cl (= tptp.mweakly_connected tptp.mweakly_connected)) :rule refl)
% 0.78/1.01 (anchor :step t2.t20 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t20.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t20.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T)))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))) :rule all_simplify)
% 0.78/1.01 (step t2.t20 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) :rule bind)
% 0.78/1.01 (step t2.t21 (cl (= (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))))) :rule cong :premises (t2.t19 t2.t20))
% 0.78/1.01 (step t2.t22 (cl (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) :rule resolution :premises (t2.t18 t2.t21 a25))
% 0.78/1.01 (step t2.t23 (cl (not (= (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))) (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))))) (not (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T)))))))) (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t24 (cl (= tptp.mweakly_dense tptp.mweakly_dense)) :rule refl)
% 0.78/1.01 (anchor :step t2.t25 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t25.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (anchor :step t2.t25.t2 :args ((S $$unsorted) (:= S S) (T $$unsorted) (:= T T) (U $$unsorted) (:= U U)))
% 0.78/1.01 (step t2.t25.t2.t1 (cl (= S S)) :rule refl)
% 0.78/1.01 (step t2.t25.t2.t2 (cl (= T T)) :rule refl)
% 0.78/1.01 (step t2.t25.t2.t3 (cl (= U U)) :rule refl)
% 0.78/1.01 (step t2.t25.t2.t4 (cl (= (@ (@ R S) T) (@ (@ R S) T))) :rule refl)
% 0.78/1.01 (step t2.t25.t2.t5 (cl (= (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))) (not (forall ((U $$unsorted)) (not (and (@ (@ R S) U) (@ (@ R U) T))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t25.t2.t6 (cl (= (forall ((U $$unsorted)) (not (and (@ (@ R S) U) (@ (@ R U) T)))) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t25.t2.t7 (cl (= (not (forall ((U $$unsorted)) (not (and (@ (@ R S) U) (@ (@ R U) T))))) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))) :rule cong :premises (t2.t25.t2.t6))
% 0.78/1.01 (step t2.t25.t2.t8 (cl (= (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))) :rule trans :premises (t2.t25.t2.t5 t2.t25.t2.t7))
% 0.78/1.01 (step t2.t25.t2.t9 (cl (= (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T)))) (=> (@ (@ R S) T) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))))) :rule cong :premises (t2.t25.t2.t4 t2.t25.t2.t8))
% 0.78/1.01 (step t2.t25.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) :rule bind)
% 0.78/1.01 (step t2.t25.t3 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t25.t4 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t25.t5 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) :rule trans :premises (t2.t25.t3 t2.t25.t4))
% 0.78/1.01 (step t2.t25.t6 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) :rule trans :premises (t2.t25.t2 t2.t25.t5))
% 0.78/1.01 (step t2.t25 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T)))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))))))) :rule bind)
% 0.78/1.01 (step t2.t26 (cl (= (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))) (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))))) :rule cong :premises (t2.t24 t2.t25))
% 0.78/1.01 (step t2.t27 (cl (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T)))))))))) :rule resolution :premises (t2.t23 t2.t26 a24))
% 0.78/1.01 (step t2.t28 (cl (not (= (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))) (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))))))) (not (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U))))))))) (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t29 (cl (= tptp.mfunctional tptp.mfunctional)) :rule refl)
% 0.78/1.01 (anchor :step t2.t30 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t30.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (anchor :step t2.t30.t2 :args ((S $$unsorted) (:= S S)))
% 0.78/1.01 (step t2.t30.t2.t1 (cl (= S S)) :rule refl)
% 0.78/1.01 (anchor :step t2.t30.t2.t2 :args ((T $$unsorted) (:= T T)))
% 0.78/1.01 (step t2.t30.t2.t2.t1 (cl (= T T)) :rule refl)
% 0.78/1.01 (step t2.t30.t2.t2.t2 (cl (= (@ (@ R S) T) (@ (@ R S) T))) :rule refl)
% 0.78/1.01 (step t2.t30.t2.t2.t3 (cl (= (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U))) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))) :rule all_simplify)
% 0.78/1.01 (step t2.t30.t2.t2.t4 (cl (= (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))) (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))) :rule cong :premises (t2.t30.t2.t2.t2 t2.t30.t2.t2.t3))
% 0.78/1.01 (step t2.t30.t2.t2 (cl (= (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U))))) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))) :rule bind)
% 0.78/1.01 (step t2.t30.t2.t3 (cl (= (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))) (not (forall ((T $$unsorted)) (not (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t30.t2.t4 (cl (= (forall ((T $$unsorted)) (not (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))) (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t30.t2.t5 (cl (= (not (forall ((T $$unsorted)) (not (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))) :rule cong :premises (t2.t30.t2.t4))
% 0.78/1.01 (step t2.t30.t2.t6 (cl (= (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))) :rule trans :premises (t2.t30.t2.t3 t2.t30.t2.t5))
% 0.78/1.01 (step t2.t30.t2.t7 (cl (= (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U))))) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))) :rule trans :premises (t2.t30.t2.t2 t2.t30.t2.t6))
% 0.78/1.01 (step t2.t30.t2 (cl (= (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))))) :rule bind)
% 0.78/1.01 (step t2.t30 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U))))))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))))) :rule bind)
% 0.78/1.01 (step t2.t31 (cl (= (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))) (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))))))) :rule cong :premises (t2.t29 t2.t30))
% 0.78/1.01 (step t2.t32 (cl (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U))))))))))) :rule resolution :premises (t2.t28 t2.t31 a23))
% 0.78/1.01 (step t2.t33 (cl (not (= (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U))))) (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U))))))) (not (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U)))))) (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t34 (cl (= tptp.mpartially_functional tptp.mpartially_functional)) :rule refl)
% 0.78/1.01 (anchor :step t2.t35 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t35.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t35.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U))))) :rule all_simplify)
% 0.78/1.01 (step t2.t35 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U)))))) :rule bind)
% 0.78/1.01 (step t2.t36 (cl (= (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (= T U))))) (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U))))))) :rule cong :premises (t2.t34 t2.t35))
% 0.78/1.01 (step t2.t37 (cl (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U)))))) :rule resolution :premises (t2.t33 t2.t36 a22))
% 0.78/1.01 (step t2.t38 (cl (not (= (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U))))) (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U))))))) (not (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U)))))) (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t39 (cl (= tptp.meuclidean tptp.meuclidean)) :rule refl)
% 0.78/1.01 (anchor :step t2.t40 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t40.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t40.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U))))) :rule all_simplify)
% 0.78/1.01 (step t2.t40 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U)))))) :rule bind)
% 0.78/1.01 (step t2.t41 (cl (= (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R S) U)) (@ (@ R T) U))))) (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U))))))) :rule cong :premises (t2.t39 t2.t40))
% 0.78/1.01 (step t2.t42 (cl (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U)))))) :rule resolution :premises (t2.t38 t2.t41 a21))
% 0.78/1.01 (step t2.t43 (cl (not (= (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U))))) (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U))))))) (not (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U)))))) (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t44 (cl (= tptp.mtransitive tptp.mtransitive)) :rule refl)
% 0.78/1.01 (anchor :step t2.t45 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t45.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t45.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U))))) :rule all_simplify)
% 0.78/1.01 (step t2.t45 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U)))))) :rule bind)
% 0.78/1.01 (step t2.t46 (cl (= (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (@ (@ R S) T) (@ (@ R T) U)) (@ (@ R S) U))))) (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U))))))) :rule cong :premises (t2.t44 t2.t45))
% 0.78/1.01 (step t2.t47 (cl (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U)))))) :rule resolution :premises (t2.t43 t2.t46 a20))
% 0.78/1.01 (step t2.t48 (cl (not (= (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))) (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T))))))))) (not (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T)))))) (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T)))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t49 (cl (= tptp.mserial tptp.mserial)) :rule refl)
% 0.78/1.01 (anchor :step t2.t50 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t50.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (anchor :step t2.t50.t2 :args ((S $$unsorted) (:= S S)))
% 0.78/1.01 (step t2.t50.t2.t1 (cl (= S S)) :rule refl)
% 0.78/1.01 (step t2.t50.t2.t2 (cl (= (exists ((T $$unsorted)) (@ (@ R S) T)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t50.t2 (cl (= (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T))))))) :rule bind)
% 0.78/1.01 (step t2.t50 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T)))))))) :rule bind)
% 0.78/1.01 (step t2.t51 (cl (= (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))) (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T))))))))) :rule cong :premises (t2.t49 t2.t50))
% 0.78/1.01 (step t2.t52 (cl (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T)))))))) :rule resolution :premises (t2.t48 t2.t51 a19))
% 0.78/1.01 (step t2.t53 (cl (not (= (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))) (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S))))))) (not (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S)))))) (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S)))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t54 (cl (= tptp.msymmetric tptp.msymmetric)) :rule refl)
% 0.78/1.01 (anchor :step t2.t55 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.78/1.01 (step t2.t55.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t55.t2 (cl (= (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S))))) :rule all_simplify)
% 0.78/1.01 (step t2.t55 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S)))) (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S)))))) :rule bind)
% 0.78/1.01 (step t2.t56 (cl (= (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))) (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S))))))) :rule cong :premises (t2.t54 t2.t55))
% 0.78/1.01 (step t2.t57 (cl (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S)))))) :rule resolution :premises (t2.t53 t2.t56 a18))
% 0.78/1.01 (step t2.t58 (cl (not (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))))) (not (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0)))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V)))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t59 (cl (= tptp.mdia tptp.mdia)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (Phi (-> $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t1 (cl (= R R)) :rule refl)
% 0.78/1.01 (step t2.t60.t2 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t4 (cl (and (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t5 (cl (not (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) (not (= tptp.mfalse (@ tptp.mnot tptp.mtrue))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t6 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.78/1.01 (step t2.t60.t7 (cl (and (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t8 (cl (not (= (= tptp.mtrue (lambda ((W $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((W $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t9 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.78/1.01 (step t2.t60.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t11 (cl (= (= tptp.mtrue (lambda ((W $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) :rule cong :premises (t2.t60.t9 t2.t60.t10))
% 0.78/1.01 (step t2.t60.t12 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule resolution :premises (t2.t60.t8 t2.t60.t11 a13))
% 0.78/1.01 (step t2.t60.t13 (cl (not (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t14 (cl (= tptp.mexists_prop tptp.mexists_prop)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15 :args ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t3 (cl (and (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t4 (cl (not (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t5 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t3 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t4 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t5 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t6 t2.t60.t15.t6.t6.t7.t7.t7.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t7 t2.t60.t15.t6.t6.t7.t7.t7.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t6 t2.t60.t15.t6.t6.t7.t7.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t10 t2.t60.t15.t6.t6.t7.t7.t7.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t6 t2.t60.t15.t6.t6.t7.t7.t7.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t7.t14 t2.t60.t15.t6.t6.t7.t7.t7.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t6 t2.t60.t15.t6.t6.t7.t7.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t5 t2.t60.t15.t6.t6.t7.t7.t7.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t3 t2.t60.t15.t6.t6.t7.t7.t7.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t8 t2.t60.t15.t6.t6.t7.t7.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t7 t2.t60.t15.t6.t6.t7.t7.t7.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t11 t2.t60.t15.t6.t6.t7.t7.t7.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t2 t2.t60.t15.t6.t6.t7.t7.t7.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t14 t2.t60.t15.t6.t6.t7.t7.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t13 t2.t60.t15.t6.t6.t7.t7.t7.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t4 t2.t60.t15.t6.t6.t7.t7.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t19 t2.t60.t15.t6.t6.t7.t7.t7.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t18 t2.t60.t15.t6.t6.t7.t7.t7.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t22 t2.t60.t15.t6.t6.t7.t7.t7.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t10.t24 t2.t60.t15.t6.t6.t7.t7.t7.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t9 t2.t60.t15.t6.t6.t7.t7.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t7.t8 t2.t60.t15.t6.t6.t7.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t7.t5 t2.t60.t15.t6.t6.t7.t7.t7.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t7.t4 t2.t60.t15.t6.t6.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t16 t2.t60.t15.t6.t6.t7.t7.t7.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t15 t2.t60.t15.t6.t6.t7.t7.t7.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t19 t2.t60.t15.t6.t6.t7.t7.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t7.t21 t2.t60.t15.t6.t6.t7.t7.t7.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t6 t2.t60.t15.t6.t6.t7.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t10.t4 t2.t60.t15.t6.t6.t7.t7.t10.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t10.t8.t3 t2.t60.t15.t6.t6.t7.t7.t10.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t10.t7 t2.t60.t15.t6.t6.t7.t7.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t10.t6 t2.t60.t15.t6.t6.t7.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t10.t10 t2.t60.t15.t6.t6.t7.t7.t10.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t10.t12 t2.t60.t15.t6.t6.t7.t7.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t10.t14 t2.t60.t15.t6.t6.t7.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t10.t16 t2.t60.t15.t6.t6.t7.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t9 t2.t60.t15.t6.t6.t7.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t8 t2.t60.t15.t6.t6.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t5 t2.t60.t15.t6.t6.t7.t7.t12 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t6 t2.t60.t15.t6.t6.t7.t7.t16.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t7 t2.t60.t15.t6.t6.t7.t7.t16.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t6 t2.t60.t15.t6.t6.t7.t7.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t10 t2.t60.t15.t6.t6.t7.t7.t16.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t6 t2.t60.t15.t6.t6.t7.t7.t16.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t16.t14 t2.t60.t15.t6.t6.t7.t7.t16.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t15 t2.t60.t15.t6.t6.t7.t7.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t5 t2.t60.t15.t6.t6.t7.t7.t19.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t9.t3 t2.t60.t15.t6.t6.t7.t7.t19.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t8 t2.t60.t15.t6.t6.t7.t7.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t7 t2.t60.t15.t6.t6.t7.t7.t19.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t11 t2.t60.t15.t6.t6.t7.t7.t19.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t15.t2 t2.t60.t15.t6.t6.t7.t7.t19.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t14 t2.t60.t15.t6.t6.t7.t7.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t13 t2.t60.t15.t6.t6.t7.t7.t19.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t4 t2.t60.t15.t6.t6.t7.t7.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t19 t2.t60.t15.t6.t6.t7.t7.t19.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t18 t2.t60.t15.t6.t6.t7.t7.t19.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t19.t22 t2.t60.t15.t6.t6.t7.t7.t19.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t19.t24 t2.t60.t15.t6.t6.t7.t7.t19.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t18 t2.t60.t15.t6.t6.t7.t7.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t7.t17 t2.t60.t15.t6.t6.t7.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t14 t2.t60.t15.t6.t6.t7.t7.t21 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t7.t4 t2.t60.t15.t6.t6.t7.t7.t13 t2.t60.t15.t6.t6.t7.t7.t22 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t7.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t25 t2.t60.t15.t6.t6.t7.t7.t26))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t24 t2.t60.t15.t6.t6.t7.t7.t27))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t28 t2.t60.t15.t6.t6.t7.t7.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t7.t30 t2.t60.t15.t6.t6.t7.t7.t31))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t6 t2.t60.t15.t6.t6.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t10.t4 t2.t60.t15.t6.t6.t7.t10.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t10.t8.t3 t2.t60.t15.t6.t6.t7.t10.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t10.t7 t2.t60.t15.t6.t6.t7.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t10.t6 t2.t60.t15.t6.t6.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t10.t10 t2.t60.t15.t6.t6.t7.t10.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t10.t12 t2.t60.t15.t6.t6.t7.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t10.t14 t2.t60.t15.t6.t6.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t10.t16 t2.t60.t15.t6.t6.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t9 t2.t60.t15.t6.t6.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t8 t2.t60.t15.t6.t6.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t5 t2.t60.t15.t6.t6.t7.t12 a6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t16.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t16.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t6 t2.t60.t15.t6.t6.t7.t16.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t7 t2.t60.t15.t6.t6.t7.t16.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t6 t2.t60.t15.t6.t6.t7.t16.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t10 t2.t60.t15.t6.t6.t7.t16.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t6 t2.t60.t15.t6.t6.t7.t16.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t7.t14 t2.t60.t15.t6.t6.t7.t16.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t6 t2.t60.t15.t6.t6.t7.t16.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t5 t2.t60.t15.t6.t6.t7.t16.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t9.t3 t2.t60.t15.t6.t6.t7.t16.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t8 t2.t60.t15.t6.t6.t7.t16.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t7 t2.t60.t15.t6.t6.t7.t16.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t11 t2.t60.t15.t6.t6.t7.t16.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t15.t2 t2.t60.t15.t6.t6.t7.t16.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t14 t2.t60.t15.t6.t6.t7.t16.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t13 t2.t60.t15.t6.t6.t7.t16.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t4 t2.t60.t15.t6.t6.t7.t16.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t19 t2.t60.t15.t6.t6.t7.t16.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t18 t2.t60.t15.t6.t6.t7.t16.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t10.t22 t2.t60.t15.t6.t6.t7.t16.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t10.t24 t2.t60.t15.t6.t6.t7.t16.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t9 t2.t60.t15.t6.t6.t7.t16.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t16.t8 t2.t60.t15.t6.t6.t7.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t16.t5 t2.t60.t15.t6.t6.t7.t16.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t16.t4 t2.t60.t15.t6.t6.t7.t16.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t16.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t16.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t16 t2.t60.t15.t6.t6.t7.t16.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t15 t2.t60.t15.t6.t6.t7.t16.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t19 t2.t60.t15.t6.t6.t7.t16.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t16.t21 t2.t60.t15.t6.t6.t7.t16.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t15 t2.t60.t15.t6.t6.t7.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t19.t4 t2.t60.t15.t6.t6.t7.t19.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t19.t8.t3 t2.t60.t15.t6.t6.t7.t19.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t19.t7 t2.t60.t15.t6.t6.t7.t19.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t19.t6 t2.t60.t15.t6.t6.t7.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t19.t10 t2.t60.t15.t6.t6.t7.t19.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t19.t12 t2.t60.t15.t6.t6.t7.t19.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t19.t14 t2.t60.t15.t6.t6.t7.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t19.t16 t2.t60.t15.t6.t6.t7.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t18 t2.t60.t15.t6.t6.t7.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t17 t2.t60.t15.t6.t6.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t14 t2.t60.t15.t6.t6.t7.t21 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t25.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t25.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t25.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t6 t2.t60.t15.t6.t6.t7.t25.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t7 t2.t60.t15.t6.t6.t7.t25.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t6 t2.t60.t15.t6.t6.t7.t25.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t10 t2.t60.t15.t6.t6.t7.t25.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t6 t2.t60.t15.t6.t6.t7.t25.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t25.t14 t2.t60.t15.t6.t6.t7.t25.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t24 t2.t60.t15.t6.t6.t7.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t5 t2.t60.t15.t6.t6.t7.t28.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t9.t3 t2.t60.t15.t6.t6.t7.t28.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t8 t2.t60.t15.t6.t6.t7.t28.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t7 t2.t60.t15.t6.t6.t7.t28.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t11 t2.t60.t15.t6.t6.t7.t28.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t15.t2 t2.t60.t15.t6.t6.t7.t28.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t14 t2.t60.t15.t6.t6.t7.t28.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t13 t2.t60.t15.t6.t6.t7.t28.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t4 t2.t60.t15.t6.t6.t7.t28.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t19 t2.t60.t15.t6.t6.t7.t28.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t18 t2.t60.t15.t6.t6.t7.t28.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t28.t22 t2.t60.t15.t6.t6.t7.t28.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t28.t24 t2.t60.t15.t6.t6.t7.t28.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t27 t2.t60.t15.t6.t6.t7.t28))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t7.t26 t2.t60.t15.t6.t6.t7.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t23 t2.t60.t15.t6.t6.t7.t30 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t7.t4 t2.t60.t15.t6.t6.t7.t13 t2.t60.t15.t6.t6.t7.t22 t2.t60.t15.t6.t6.t7.t31 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t32))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t15.t6.t6.t7.t32))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t34 t2.t60.t15.t6.t6.t7.t35))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t36 t2.t60.t15.t6.t6.t7.t37))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t33 t2.t60.t15.t6.t6.t7.t38))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t34 t2.t60.t15.t6.t6.t7.t37))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t40 t2.t60.t15.t6.t6.t7.t35))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t39 t2.t60.t15.t6.t6.t7.t41))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t7.t42 t2.t60.t15.t6.t6.t7.t43))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t6 t2.t60.t15.t6.t6.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t5 t2.t60.t15.t6.t6.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t7 t2.t60.t15.t6.t6.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t4 t2.t60.t15.t6.t6.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t12.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t12.t4 t2.t60.t15.t6.t6.t10.t12.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t12.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t11 t2.t60.t15.t6.t6.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t10 t2.t60.t15.t6.t6.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t15 t2.t60.t15.t6.t6.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t17 t2.t60.t15.t6.t6.t10.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t14 t2.t60.t15.t6.t6.t10.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t22.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t22.t2 t2.t60.t15.t6.t6.t10.t22.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t22.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t21 t2.t60.t15.t6.t6.t10.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t20 t2.t60.t15.t6.t6.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t10.t24 t2.t60.t15.t6.t6.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t6.t10.t26 t2.t60.t15.t6.t6.t10.t27))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t6.t6.t9 t2.t60.t15.t6.t6.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t15.t6.t6.t8 t2.t60.t15.t6.t6.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t5 t2.t60.t15.t6.t6.t12 a7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t6 t2.t60.t15.t6.t6.t16.t7.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t7 t2.t60.t15.t6.t6.t16.t7.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t6 t2.t60.t15.t6.t6.t16.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t10 t2.t60.t15.t6.t6.t16.t7.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t6 t2.t60.t15.t6.t6.t16.t7.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t7.t14 t2.t60.t15.t6.t6.t16.t7.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t6 t2.t60.t15.t6.t6.t16.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t5 t2.t60.t15.t6.t6.t16.t7.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t9.t3 t2.t60.t15.t6.t6.t16.t7.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t8 t2.t60.t15.t6.t6.t16.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t7 t2.t60.t15.t6.t6.t16.t7.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t11 t2.t60.t15.t6.t6.t16.t7.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t15.t2 t2.t60.t15.t6.t6.t16.t7.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t14 t2.t60.t15.t6.t6.t16.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t13 t2.t60.t15.t6.t6.t16.t7.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t4 t2.t60.t15.t6.t6.t16.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t19 t2.t60.t15.t6.t6.t16.t7.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t18 t2.t60.t15.t6.t6.t16.t7.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t10.t22 t2.t60.t15.t6.t6.t16.t7.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t10.t24 t2.t60.t15.t6.t6.t16.t7.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t9 t2.t60.t15.t6.t6.t16.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t7.t8 t2.t60.t15.t6.t6.t16.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t7.t5 t2.t60.t15.t6.t6.t16.t7.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t7.t4 t2.t60.t15.t6.t6.t16.t7.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t16 t2.t60.t15.t6.t6.t16.t7.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t15 t2.t60.t15.t6.t6.t16.t7.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t19 t2.t60.t15.t6.t6.t16.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t7.t21 t2.t60.t15.t6.t6.t16.t7.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t6 t2.t60.t15.t6.t6.t16.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t10.t4 t2.t60.t15.t6.t6.t16.t10.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t10.t8.t3 t2.t60.t15.t6.t6.t16.t10.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t10.t7 t2.t60.t15.t6.t6.t16.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t10.t6 t2.t60.t15.t6.t6.t16.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t10.t10 t2.t60.t15.t6.t6.t16.t10.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t10.t12 t2.t60.t15.t6.t6.t16.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t10.t14 t2.t60.t15.t6.t6.t16.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t10.t16 t2.t60.t15.t6.t6.t16.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t9 t2.t60.t15.t6.t6.t16.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t8 t2.t60.t15.t6.t6.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t5 t2.t60.t15.t6.t6.t16.t12 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t16.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t6 t2.t60.t15.t6.t6.t16.t16.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t7 t2.t60.t15.t6.t6.t16.t16.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t6 t2.t60.t15.t6.t6.t16.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t10 t2.t60.t15.t6.t6.t16.t16.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t6 t2.t60.t15.t6.t6.t16.t16.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t16.t14 t2.t60.t15.t6.t6.t16.t16.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t15 t2.t60.t15.t6.t6.t16.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t5 t2.t60.t15.t6.t6.t16.t19.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t9.t3 t2.t60.t15.t6.t6.t16.t19.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t8 t2.t60.t15.t6.t6.t16.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t7 t2.t60.t15.t6.t6.t16.t19.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t11 t2.t60.t15.t6.t6.t16.t19.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t15.t2 t2.t60.t15.t6.t6.t16.t19.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t14 t2.t60.t15.t6.t6.t16.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t13 t2.t60.t15.t6.t6.t16.t19.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t4 t2.t60.t15.t6.t6.t16.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t19 t2.t60.t15.t6.t6.t16.t19.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t18 t2.t60.t15.t6.t6.t16.t19.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t19.t22 t2.t60.t15.t6.t6.t16.t19.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t19.t24 t2.t60.t15.t6.t6.t16.t19.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t18 t2.t60.t15.t6.t6.t16.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t16.t17 t2.t60.t15.t6.t6.t16.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t14 t2.t60.t15.t6.t6.t16.t21 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t16.t4 t2.t60.t15.t6.t6.t16.t13 t2.t60.t15.t6.t6.t16.t22 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t16.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t25 t2.t60.t15.t6.t6.t16.t26))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t24 t2.t60.t15.t6.t6.t16.t27))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t28 t2.t60.t15.t6.t6.t16.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t16.t30 t2.t60.t15.t6.t6.t16.t31))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t15 t2.t60.t15.t6.t6.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t19.t4 t2.t60.t15.t6.t6.t19.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t19.t8.t3 t2.t60.t15.t6.t6.t19.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t19.t7 t2.t60.t15.t6.t6.t19.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t19.t6 t2.t60.t15.t6.t6.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t19.t10 t2.t60.t15.t6.t6.t19.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t19.t12 t2.t60.t15.t6.t6.t19.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t19.t14 t2.t60.t15.t6.t6.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t19.t16 t2.t60.t15.t6.t6.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t18 t2.t60.t15.t6.t6.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t17 t2.t60.t15.t6.t6.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t14 t2.t60.t15.t6.t6.t21 a6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t25.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t25.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t25.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t6 t2.t60.t15.t6.t6.t25.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t7 t2.t60.t15.t6.t6.t25.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t6 t2.t60.t15.t6.t6.t25.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t10 t2.t60.t15.t6.t6.t25.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t6 t2.t60.t15.t6.t6.t25.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t7.t14 t2.t60.t15.t6.t6.t25.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t6 t2.t60.t15.t6.t6.t25.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t5 t2.t60.t15.t6.t6.t25.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t9.t3 t2.t60.t15.t6.t6.t25.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t8 t2.t60.t15.t6.t6.t25.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t7 t2.t60.t15.t6.t6.t25.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t11 t2.t60.t15.t6.t6.t25.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t15.t2 t2.t60.t15.t6.t6.t25.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t14 t2.t60.t15.t6.t6.t25.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t13 t2.t60.t15.t6.t6.t25.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t4 t2.t60.t15.t6.t6.t25.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t19 t2.t60.t15.t6.t6.t25.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t18 t2.t60.t15.t6.t6.t25.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t10.t22 t2.t60.t15.t6.t6.t25.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t10.t24 t2.t60.t15.t6.t6.t25.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t9 t2.t60.t15.t6.t6.t25.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t25.t8 t2.t60.t15.t6.t6.t25.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t25.t5 t2.t60.t15.t6.t6.t25.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t25.t4 t2.t60.t15.t6.t6.t25.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t25.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t25.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t16 t2.t60.t15.t6.t6.t25.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t15 t2.t60.t15.t6.t6.t25.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t19 t2.t60.t15.t6.t6.t25.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t25.t21 t2.t60.t15.t6.t6.t25.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t24 t2.t60.t15.t6.t6.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t28.t4 t2.t60.t15.t6.t6.t28.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t28.t8.t3 t2.t60.t15.t6.t6.t28.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t28.t7 t2.t60.t15.t6.t6.t28.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t28.t6 t2.t60.t15.t6.t6.t28.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t28.t10 t2.t60.t15.t6.t6.t28.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t28.t12 t2.t60.t15.t6.t6.t28.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t28.t14 t2.t60.t15.t6.t6.t28.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t6.t28.t16 t2.t60.t15.t6.t6.t28.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t6.t27 t2.t60.t15.t6.t6.t28))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t26 t2.t60.t15.t6.t6.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t6.t23 t2.t60.t15.t6.t6.t30 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t34.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t34.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t6.t34.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t6 t2.t60.t15.t6.t6.t34.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t7 t2.t60.t15.t6.t6.t34.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t6 t2.t60.t15.t6.t6.t34.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t10 t2.t60.t15.t6.t6.t34.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t6 t2.t60.t15.t6.t6.t34.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t34.t14 t2.t60.t15.t6.t6.t34.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t6.t33 t2.t60.t15.t6.t6.t34))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t5 t2.t60.t15.t6.t6.t37.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t9.t3 t2.t60.t15.t6.t6.t37.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t8 t2.t60.t15.t6.t6.t37.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t7 t2.t60.t15.t6.t6.t37.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t11 t2.t60.t15.t6.t6.t37.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t15.t2 t2.t60.t15.t6.t6.t37.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t14 t2.t60.t15.t6.t6.t37.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t13 t2.t60.t15.t6.t6.t37.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t4 t2.t60.t15.t6.t6.t37.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t6.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t19 t2.t60.t15.t6.t6.t37.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t18 t2.t60.t15.t6.t6.t37.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t37.t22 t2.t60.t15.t6.t6.t37.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t6.t37.t24 t2.t60.t15.t6.t6.t37.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t6.t36 t2.t60.t15.t6.t6.t37))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t6.t35 t2.t60.t15.t6.t6.t38))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t6.t32 t2.t60.t15.t6.t6.t39 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t6.t4 t2.t60.t15.t6.t6.t13 t2.t60.t15.t6.t6.t22 t2.t60.t15.t6.t6.t31 t2.t60.t15.t6.t6.t40 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t6.t41))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t60.t15.t6.t6.t41))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t44 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t60.t15.t6.t6.t43 t2.t60.t15.t6.t6.t44))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t46 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t6.t6.t45 t2.t60.t15.t6.t6.t46))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t6.t6.t42 t2.t60.t15.t6.t6.t47))
% 0.78/1.01 (step t2.t60.t15.t6.t6.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t6.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t6.t48 t2.t60.t15.t6.t6.t49))
% 0.78/1.01 (step t2.t60.t15.t6.t6 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t7 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t5 t2.t60.t15.t6.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t8 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t9 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t6 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t60.t15.t6.t9.t5 t2.t60.t15.t6.t9.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t9.t7 t2.t60.t15.t6.t9.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t6.t9.t4 t2.t60.t15.t6.t9.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t9.t12 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t60.t15.t6.t9.t12.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t60.t15.t6.t9.t12.t3 t2.t60.t15.t6.t9.t12.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t15.t6.t9.t11 t2.t60.t15.t6.t9.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t15.t6.t9.t10 t2.t60.t15.t6.t9.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t9.t14 t2.t60.t15.t6.t9.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t9.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t9.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t9.t16 t2.t60.t15.t6.t9.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t9 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t10 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t8 t2.t60.t15.t6.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t11 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t7 t2.t60.t15.t6.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t12 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t4 t2.t60.t15.t6.t11 a8))
% 0.78/1.01 (step t2.t60.t15.t6.t13 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t14 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t7.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t6 t2.t60.t15.t6.t15.t7.t7.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t7 t2.t60.t15.t6.t15.t7.t7.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t6 t2.t60.t15.t6.t15.t7.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t10 t2.t60.t15.t6.t15.t7.t7.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t6 t2.t60.t15.t6.t15.t7.t7.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t7.t14 t2.t60.t15.t6.t15.t7.t7.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t6 t2.t60.t15.t6.t15.t7.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t5 t2.t60.t15.t6.t15.t7.t7.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t9.t3 t2.t60.t15.t6.t15.t7.t7.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t8 t2.t60.t15.t6.t15.t7.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t7 t2.t60.t15.t6.t15.t7.t7.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t11 t2.t60.t15.t6.t15.t7.t7.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t15.t2 t2.t60.t15.t6.t15.t7.t7.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t14 t2.t60.t15.t6.t15.t7.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t13 t2.t60.t15.t6.t15.t7.t7.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t4 t2.t60.t15.t6.t15.t7.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t19 t2.t60.t15.t6.t15.t7.t7.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t18 t2.t60.t15.t6.t15.t7.t7.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t10.t22 t2.t60.t15.t6.t15.t7.t7.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t10.t24 t2.t60.t15.t6.t15.t7.t7.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t9 t2.t60.t15.t6.t15.t7.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t7.t8 t2.t60.t15.t6.t15.t7.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t7.t5 t2.t60.t15.t6.t15.t7.t7.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t7.t4 t2.t60.t15.t6.t15.t7.t7.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t7.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t16 t2.t60.t15.t6.t15.t7.t7.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t15 t2.t60.t15.t6.t15.t7.t7.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t19 t2.t60.t15.t6.t15.t7.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t7.t21 t2.t60.t15.t6.t15.t7.t7.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t6 t2.t60.t15.t6.t15.t7.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t10.t4 t2.t60.t15.t6.t15.t7.t10.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t10.t8.t3 t2.t60.t15.t6.t15.t7.t10.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t10.t7 t2.t60.t15.t6.t15.t7.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t10.t6 t2.t60.t15.t6.t15.t7.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t10.t10 t2.t60.t15.t6.t15.t7.t10.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t10.t12 t2.t60.t15.t6.t15.t7.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t10.t14 t2.t60.t15.t6.t15.t7.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t10.t16 t2.t60.t15.t6.t15.t7.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t9 t2.t60.t15.t6.t15.t7.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t8 t2.t60.t15.t6.t15.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t5 t2.t60.t15.t6.t15.t7.t12 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t16.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t16.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t6 t2.t60.t15.t6.t15.t7.t16.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t7 t2.t60.t15.t6.t15.t7.t16.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t6 t2.t60.t15.t6.t15.t7.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t10 t2.t60.t15.t6.t15.t7.t16.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t6 t2.t60.t15.t6.t15.t7.t16.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t16.t14 t2.t60.t15.t6.t15.t7.t16.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t15 t2.t60.t15.t6.t15.t7.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t5 t2.t60.t15.t6.t15.t7.t19.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t9.t3 t2.t60.t15.t6.t15.t7.t19.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t8 t2.t60.t15.t6.t15.t7.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t7 t2.t60.t15.t6.t15.t7.t19.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t11 t2.t60.t15.t6.t15.t7.t19.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t15.t2 t2.t60.t15.t6.t15.t7.t19.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t14 t2.t60.t15.t6.t15.t7.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t13 t2.t60.t15.t6.t15.t7.t19.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t4 t2.t60.t15.t6.t15.t7.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t19 t2.t60.t15.t6.t15.t7.t19.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t18 t2.t60.t15.t6.t15.t7.t19.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t19.t22 t2.t60.t15.t6.t15.t7.t19.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t19.t24 t2.t60.t15.t6.t15.t7.t19.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t18 t2.t60.t15.t6.t15.t7.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t15.t7.t17 t2.t60.t15.t6.t15.t7.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t14 t2.t60.t15.t6.t15.t7.t21 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t7.t4 t2.t60.t15.t6.t15.t7.t13 t2.t60.t15.t6.t15.t7.t22 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t7.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t25 t2.t60.t15.t6.t15.t7.t26))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t24 t2.t60.t15.t6.t15.t7.t27))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t28 t2.t60.t15.t6.t15.t7.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t7.t30 t2.t60.t15.t6.t15.t7.t31))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t6 t2.t60.t15.t6.t15.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t10.t4 t2.t60.t15.t6.t15.t10.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t10.t8.t3 t2.t60.t15.t6.t15.t10.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t10.t7 t2.t60.t15.t6.t15.t10.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t10.t6 t2.t60.t15.t6.t15.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t10.t10 t2.t60.t15.t6.t15.t10.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t10.t12 t2.t60.t15.t6.t15.t10.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t10.t14 t2.t60.t15.t6.t15.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t15.t10.t16 t2.t60.t15.t6.t15.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t15.t9 t2.t60.t15.t6.t15.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t8 t2.t60.t15.t6.t15.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t15.t5 t2.t60.t15.t6.t15.t12 a6))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t16.t7.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t16.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t16.t7.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t6 t2.t60.t15.t6.t15.t16.t7.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t7 t2.t60.t15.t6.t15.t16.t7.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t6 t2.t60.t15.t6.t15.t16.t7.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t10 t2.t60.t15.t6.t15.t16.t7.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t6 t2.t60.t15.t6.t15.t16.t7.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t7.t14 t2.t60.t15.t6.t15.t16.t7.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t6 t2.t60.t15.t6.t15.t16.t7))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t5 t2.t60.t15.t6.t15.t16.t10.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t9.t3 t2.t60.t15.t6.t15.t16.t10.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t8 t2.t60.t15.t6.t15.t16.t10.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t7 t2.t60.t15.t6.t15.t16.t10.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t11 t2.t60.t15.t6.t15.t16.t10.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t15.t2 t2.t60.t15.t6.t15.t16.t10.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t14 t2.t60.t15.t6.t15.t16.t10.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t13 t2.t60.t15.t6.t15.t16.t10.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t4 t2.t60.t15.t6.t15.t16.t10.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t19 t2.t60.t15.t6.t15.t16.t10.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t18 t2.t60.t15.t6.t15.t16.t10.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t10.t22 t2.t60.t15.t6.t15.t16.t10.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t10.t24 t2.t60.t15.t6.t15.t16.t10.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t9 t2.t60.t15.t6.t15.t16.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t15.t16.t8 t2.t60.t15.t6.t15.t16.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t15.t16.t5 t2.t60.t15.t6.t15.t16.t12 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t16.t4 t2.t60.t15.t6.t15.t16.t13 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t16.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t16.t14))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t16 t2.t60.t15.t6.t15.t16.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t15 t2.t60.t15.t6.t15.t16.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t19 t2.t60.t15.t6.t15.t16.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t16.t21 t2.t60.t15.t6.t15.t16.t22))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t15 t2.t60.t15.t6.t15.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t19.t4 t2.t60.t15.t6.t15.t19.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t19.t8.t3 t2.t60.t15.t6.t15.t19.t8.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t19.t7 t2.t60.t15.t6.t15.t19.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t19.t6 t2.t60.t15.t6.t15.t19.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t19.t10 t2.t60.t15.t6.t15.t19.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t19.t12 t2.t60.t15.t6.t15.t19.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t19.t14 t2.t60.t15.t6.t15.t19.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t15.t19.t16 t2.t60.t15.t6.t15.t19.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t15.t18 t2.t60.t15.t6.t15.t19))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t17 t2.t60.t15.t6.t15.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t15.t14 t2.t60.t15.t6.t15.t21 a5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t25.t4 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t15.t25.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t15.t25.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t6 t2.t60.t15.t6.t15.t25.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t7 t2.t60.t15.t6.t15.t25.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t6 t2.t60.t15.t6.t15.t25.t11))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t10 t2.t60.t15.t6.t15.t25.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t6 t2.t60.t15.t6.t15.t25.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t25.t14 t2.t60.t15.t6.t15.t25.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t15.t24 t2.t60.t15.t6.t15.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t5 t2.t60.t15.t6.t15.t28.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t9.t3 t2.t60.t15.t6.t15.t28.t9.t4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t8 t2.t60.t15.t6.t15.t28.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t7 t2.t60.t15.t6.t15.t28.t10))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t11 t2.t60.t15.t6.t15.t28.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t15.t2 t2.t60.t15.t6.t15.t28.t15.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t14 t2.t60.t15.t6.t15.t28.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t13 t2.t60.t15.t6.t15.t28.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t4 t2.t60.t15.t6.t15.t28.t17))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t15.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t20.t2))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t19 t2.t60.t15.t6.t15.t28.t20))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t18 t2.t60.t15.t6.t15.t28.t21))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t28.t22 t2.t60.t15.t6.t15.t28.t23))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t15.t28.t24 t2.t60.t15.t6.t15.t28.t25))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t15.t27 t2.t60.t15.t6.t15.t28))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t15.t26 t2.t60.t15.t6.t15.t29))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t15.t23 t2.t60.t15.t6.t15.t30 a4))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t15.t4 t2.t60.t15.t6.t15.t13 t2.t60.t15.t6.t15.t22 t2.t60.t15.t6.t15.t31 a3 a2 a1 a0))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t15.t6.t15.t32))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t15.t6.t15.t32))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t35 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t34 t2.t60.t15.t6.t15.t35))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t37 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t36 t2.t60.t15.t6.t15.t37))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t6.t15.t33 t2.t60.t15.t6.t15.t38))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t6.t15.t34 t2.t60.t15.t6.t15.t37))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t15.t6.t15.t40 t2.t60.t15.t6.t15.t35))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t15.t6.t15.t39 t2.t60.t15.t6.t15.t41))
% 0.78/1.01 (step t2.t60.t15.t6.t15.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t15.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t15.t42 t2.t60.t15.t6.t15.t43))
% 0.78/1.01 (step t2.t60.t15.t6.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t16 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t14 t2.t60.t15.t6.t15))
% 0.78/1.01 (step t2.t60.t15.t6.t17 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t6.t18.t5 t2.t60.t15.t6.t18.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t6.t18.t7 t2.t60.t15.t6.t18.t8))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t18.t4 t2.t60.t15.t6.t18.t9))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.01 (anchor :step t2.t60.t15.t6.t18.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t18.t12.t3))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t18.t12.t4 t2.t60.t15.t6.t18.t12.t5))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t18.t12.t6))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t18.t11 t2.t60.t15.t6.t18.t12))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t18.t10 t2.t60.t15.t6.t18.t13))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t16 (cl (= Phi Phi)) :rule refl)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t6.t18.t15 t2.t60.t15.t6.t18.t16))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.01 (step t2.t60.t15.t6.t18.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t6.t18.t17 t2.t60.t15.t6.t18.t18))
% 0.78/1.01 (step t2.t60.t15.t6.t18.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t18.t14 t2.t60.t15.t6.t18.t19))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t18.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t18.t22.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t18.t22.t2 t2.t60.t15.t6.t18.t22.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t15.t6.t18.t22.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t18.t21 t2.t60.t15.t6.t18.t22))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t18.t20 t2.t60.t15.t6.t18.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t18.t24 t2.t60.t15.t6.t18.t25))
% 0.78/1.02 (step t2.t60.t15.t6.t18.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t18.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t6.t18.t26 t2.t60.t15.t6.t18.t27))
% 0.78/1.02 (step t2.t60.t15.t6.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t19 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t6.t17 t2.t60.t15.t6.t18))
% 0.78/1.02 (step t2.t60.t15.t6.t20 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t15.t6.t16 t2.t60.t15.t6.t19))
% 0.78/1.02 (step t2.t60.t15.t6.t21 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t15.t6.t13 t2.t60.t15.t6.t20 a7))
% 0.78/1.02 (step t2.t60.t15.t6.t22 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t23 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t24.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t24.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t24.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t6 t2.t60.t15.t6.t24.t7.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t7 t2.t60.t15.t6.t24.t7.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t6 t2.t60.t15.t6.t24.t7.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t10 t2.t60.t15.t6.t24.t7.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t6 t2.t60.t15.t6.t24.t7.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t7.t14 t2.t60.t15.t6.t24.t7.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t6 t2.t60.t15.t6.t24.t7.t7))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t5 t2.t60.t15.t6.t24.t7.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t9.t3 t2.t60.t15.t6.t24.t7.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t8 t2.t60.t15.t6.t24.t7.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t7 t2.t60.t15.t6.t24.t7.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t11 t2.t60.t15.t6.t24.t7.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t15.t2 t2.t60.t15.t6.t24.t7.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t14 t2.t60.t15.t6.t24.t7.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t13 t2.t60.t15.t6.t24.t7.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t4 t2.t60.t15.t6.t24.t7.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t19 t2.t60.t15.t6.t24.t7.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t18 t2.t60.t15.t6.t24.t7.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t10.t22 t2.t60.t15.t6.t24.t7.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t10.t24 t2.t60.t15.t6.t24.t7.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t9 t2.t60.t15.t6.t24.t7.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t24.t7.t8 t2.t60.t15.t6.t24.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t24.t7.t5 t2.t60.t15.t6.t24.t7.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t24.t7.t4 t2.t60.t15.t6.t24.t7.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t24.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t24.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t16 t2.t60.t15.t6.t24.t7.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t15 t2.t60.t15.t6.t24.t7.t18))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t19 t2.t60.t15.t6.t24.t7.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t7.t21 t2.t60.t15.t6.t24.t7.t22))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t24.t6 t2.t60.t15.t6.t24.t7))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t10.t4 t2.t60.t15.t6.t24.t10.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t24.t10.t8.t3 t2.t60.t15.t6.t24.t10.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t10.t7 t2.t60.t15.t6.t24.t10.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t10.t6 t2.t60.t15.t6.t24.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t24.t10.t10 t2.t60.t15.t6.t24.t10.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t10.t12 t2.t60.t15.t6.t24.t10.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t10.t14 t2.t60.t15.t6.t24.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t24.t10.t16 t2.t60.t15.t6.t24.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t24.t9 t2.t60.t15.t6.t24.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t24.t8 t2.t60.t15.t6.t24.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t24.t5 t2.t60.t15.t6.t24.t12 a5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t24.t16.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t24.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t24.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t6 t2.t60.t15.t6.t24.t16.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t7 t2.t60.t15.t6.t24.t16.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t6 t2.t60.t15.t6.t24.t16.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t10 t2.t60.t15.t6.t24.t16.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t6 t2.t60.t15.t6.t24.t16.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t16.t14 t2.t60.t15.t6.t24.t16.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t24.t15 t2.t60.t15.t6.t24.t16))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t5 t2.t60.t15.t6.t24.t19.t6))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t9.t3 t2.t60.t15.t6.t24.t19.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t8 t2.t60.t15.t6.t24.t19.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t7 t2.t60.t15.t6.t24.t19.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t11 t2.t60.t15.t6.t24.t19.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t15.t2 t2.t60.t15.t6.t24.t19.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t14 t2.t60.t15.t6.t24.t19.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t13 t2.t60.t15.t6.t24.t19.t16))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t4 t2.t60.t15.t6.t24.t19.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t24.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t19 t2.t60.t15.t6.t24.t19.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t18 t2.t60.t15.t6.t24.t19.t21))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t19.t22 t2.t60.t15.t6.t24.t19.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t24.t19.t24 t2.t60.t15.t6.t24.t19.t25))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t24.t18 t2.t60.t15.t6.t24.t19))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t24.t17 t2.t60.t15.t6.t24.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t24.t14 t2.t60.t15.t6.t24.t21 a4))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t24.t4 t2.t60.t15.t6.t24.t13 t2.t60.t15.t6.t24.t22 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t24.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t24.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t24.t25 t2.t60.t15.t6.t24.t26))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t24.t24 t2.t60.t15.t6.t24.t27))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t6.t24.t28 t2.t60.t15.t6.t24.t29))
% 0.78/1.02 (step t2.t60.t15.t6.t24.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t24.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t24.t30 t2.t60.t15.t6.t24.t31))
% 0.78/1.02 (step t2.t60.t15.t6.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t25 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t23 t2.t60.t15.t6.t24))
% 0.78/1.02 (step t2.t60.t15.t6.t26 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t27.t4 t2.t60.t15.t6.t27.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t27.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t27.t8.t3 t2.t60.t15.t6.t27.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t27.t7 t2.t60.t15.t6.t27.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t27.t6 t2.t60.t15.t6.t27.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t27.t10 t2.t60.t15.t6.t27.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t6.t27.t12 t2.t60.t15.t6.t27.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t27.t14 t2.t60.t15.t6.t27.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t27.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t27.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t27.t16 t2.t60.t15.t6.t27.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t28 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t26 t2.t60.t15.t6.t27))
% 0.78/1.02 (step t2.t60.t15.t6.t29 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t25 t2.t60.t15.t6.t28))
% 0.78/1.02 (step t2.t60.t15.t6.t30 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t22 t2.t60.t15.t6.t29 a6))
% 0.78/1.02 (step t2.t60.t15.t6.t31 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t32 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t33.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t33.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t33.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t6 t2.t60.t15.t6.t33.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t7 t2.t60.t15.t6.t33.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t6 t2.t60.t15.t6.t33.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t10 t2.t60.t15.t6.t33.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t6 t2.t60.t15.t6.t33.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t33.t7.t14 t2.t60.t15.t6.t33.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t33.t6 t2.t60.t15.t6.t33.t7))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t5 t2.t60.t15.t6.t33.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t9.t3 t2.t60.t15.t6.t33.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t8 t2.t60.t15.t6.t33.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t7 t2.t60.t15.t6.t33.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t11 t2.t60.t15.t6.t33.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t15.t2 t2.t60.t15.t6.t33.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t14 t2.t60.t15.t6.t33.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t13 t2.t60.t15.t6.t33.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t4 t2.t60.t15.t6.t33.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t33.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t19 t2.t60.t15.t6.t33.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t18 t2.t60.t15.t6.t33.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t33.t10.t22 t2.t60.t15.t6.t33.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t33.t10.t24 t2.t60.t15.t6.t33.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t33.t9 t2.t60.t15.t6.t33.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t33.t8 t2.t60.t15.t6.t33.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t33.t5 t2.t60.t15.t6.t33.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t33.t4 t2.t60.t15.t6.t33.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t33.t14))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t33.t14))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t33.t16 t2.t60.t15.t6.t33.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t33.t15 t2.t60.t15.t6.t33.t18))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t6.t33.t19 t2.t60.t15.t6.t33.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t33.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t33.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t33.t21 t2.t60.t15.t6.t33.t22))
% 0.78/1.02 (step t2.t60.t15.t6.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t34 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t32 t2.t60.t15.t6.t33))
% 0.78/1.02 (step t2.t60.t15.t6.t35 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t36.t4 t2.t60.t15.t6.t36.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t36.t8.t3 t2.t60.t15.t6.t36.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t36.t7 t2.t60.t15.t6.t36.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t36.t6 t2.t60.t15.t6.t36.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t36.t10 t2.t60.t15.t6.t36.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t36.t12 t2.t60.t15.t6.t36.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t36.t14 t2.t60.t15.t6.t36.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t6.t36.t16 t2.t60.t15.t6.t36.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t37 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t35 t2.t60.t15.t6.t36))
% 0.78/1.02 (step t2.t60.t15.t6.t38 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t34 t2.t60.t15.t6.t37))
% 0.78/1.02 (step t2.t60.t15.t6.t39 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t6.t31 t2.t60.t15.t6.t38 a5))
% 0.78/1.02 (step t2.t60.t15.t6.t40 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t6.t41 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t42.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t42.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t6.t42.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t6.t42.t6 t2.t60.t15.t6.t42.t8))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t6.t42.t7 t2.t60.t15.t6.t42.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t6.t42.t6 t2.t60.t15.t6.t42.t11))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t6.t42.t10 t2.t60.t15.t6.t42.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t6.t42.t6 t2.t60.t15.t6.t42.t13))
% 0.78/1.02 (step t2.t60.t15.t6.t42.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t42.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t42.t14 t2.t60.t15.t6.t42.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t43 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t41 t2.t60.t15.t6.t42))
% 0.78/1.02 (step t2.t60.t15.t6.t44 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t6.t45.t5 t2.t60.t15.t6.t45.t6))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t45.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t6.t45.t9.t3 t2.t60.t15.t6.t45.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t45.t8 t2.t60.t15.t6.t45.t9))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t6.t45.t7 t2.t60.t15.t6.t45.t10))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t45.t11 t2.t60.t15.t6.t45.t12))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t45.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t6.t45.t15.t2 t2.t60.t15.t6.t45.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t45.t14 t2.t60.t15.t6.t45.t15))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t6.t45.t13 t2.t60.t15.t6.t45.t16))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t6.t45.t4 t2.t60.t15.t6.t45.t17))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t45.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t6.t45.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t45.t19 t2.t60.t15.t6.t45.t20))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t6.t45.t18 t2.t60.t15.t6.t45.t21))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t45.t22 t2.t60.t15.t6.t45.t23))
% 0.78/1.02 (step t2.t60.t15.t6.t45.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t6.t45.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t6.t45.t24 t2.t60.t15.t6.t45.t25))
% 0.78/1.02 (step t2.t60.t15.t6.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t46 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t6.t44 t2.t60.t15.t6.t45))
% 0.78/1.02 (step t2.t60.t15.t6.t47 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t6.t43 t2.t60.t15.t6.t46))
% 0.78/1.02 (step t2.t60.t15.t6.t48 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t6.t40 t2.t60.t15.t6.t47 a4))
% 0.78/1.02 (step t2.t60.t15.t6.t49 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t6.t3 a10 a9 t2.t60.t15.t6.t12 t2.t60.t15.t6.t21 t2.t60.t15.t6.t30 t2.t60.t15.t6.t39 t2.t60.t15.t6.t48 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t6.t50 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t6.t49))
% 0.78/1.02 (step t2.t60.t15.t6.t51 (cl (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule and :premises (t2.t60.t15.t6.t49))
% 0.78/1.02 (anchor :step t2.t60.t15.t6.t52 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t6.t52.t1 (cl (= X X)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t52.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t52.t3 (cl (= (@ Phi X) (@ Phi X))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t52.t4 (cl (= (@ tptp.mnot (@ Phi X)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)))) :rule cong :premises (t2.t60.t15.t6.t50 t2.t60.t15.t6.t52.t3))
% 0.78/1.02 (step t2.t60.t15.t6.t52.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t52.t6 (cl (= (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t52.t4 t2.t60.t15.t6.t52.t5))
% 0.78/1.02 (step t2.t60.t15.t6.t52 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t6.t53 (cl (= (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t6.t51 t2.t60.t15.t6.t52))
% 0.78/1.02 (step t2.t60.t15.t6.t54 (cl (= (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t6.t50 t2.t60.t15.t6.t53))
% 0.78/1.02 (step t2.t60.t15.t6.t55 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t6.t56 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t6.t54 t2.t60.t15.t6.t55))
% 0.78/1.02 (step t2.t60.t15.t6 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t7 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t5 t2.t60.t15.t6))
% 0.78/1.02 (step t2.t60.t15.t8 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t9 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t4 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t9.t5 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t9.t5.t1 (cl (= X X)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t9.t5.t3 t2.t60.t15.t9.t5.t4))
% 0.78/1.02 (step t2.t60.t15.t9.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t9.t5.t5 t2.t60.t15.t9.t5.t6))
% 0.78/1.02 (step t2.t60.t15.t9.t5 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t9.t6 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t9.t4 t2.t60.t15.t9.t5))
% 0.78/1.02 (step t2.t60.t15.t9.t7 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t9.t8 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t9.t8.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t9.t8.t2 :args ((X tptp.mu) (:= X X)))
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t1 (cl (= X X)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t2 (cl (= (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t4 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W))) :rule cong :premises (t2.t60.t15.t9.t8.t2.t2 t2.t60.t15.t9.t8.t2.t3))
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W) (not (@ (@ Phi X) W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2.t6 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (not (@ (@ Phi X) W)))) :rule trans :premises (t2.t60.t15.t9.t8.t2.t4 t2.t60.t15.t9.t8.t2.t5))
% 0.78/1.02 (step t2.t60.t15.t9.t8.t2 (cl (= (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t9.t8 (cl (= (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t9.t9 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t60.t15.t9.t7 t2.t60.t15.t9.t8))
% 0.78/1.02 (step t2.t60.t15.t9.t10 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t60.t15.t9.t6 t2.t60.t15.t9.t9))
% 0.78/1.02 (step t2.t60.t15.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule cong :premises (t2.t60.t15.t9.t3 t2.t60.t15.t9.t10))
% 0.78/1.02 (step t2.t60.t15.t9.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t9.t13 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t9.t13.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule cong :premises (t2.t60.t15.t9.t13.t2))
% 0.78/1.02 (step t2.t60.t15.t9.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t60.t15.t9.t12 t2.t60.t15.t9.t13))
% 0.78/1.02 (step t2.t60.t15.t9.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t60.t15.t9.t11 t2.t60.t15.t9.t14))
% 0.78/1.02 (step t2.t60.t15.t9.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t9.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t9.t15 t2.t60.t15.t9.t16))
% 0.78/1.02 (step t2.t60.t15.t9.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t9.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t9.t17 t2.t60.t15.t9.t18))
% 0.78/1.02 (step t2.t60.t15.t9 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t10 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t8 t2.t60.t15.t9))
% 0.78/1.02 (step t2.t60.t15.t11 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t7 t2.t60.t15.t10))
% 0.78/1.02 (step t2.t60.t15.t12 (cl (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t4 t2.t60.t15.t11 a11))
% 0.78/1.02 (step t2.t60.t15.t13 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t14 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t6 t2.t60.t15.t15.t7.t7.t7.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t7 t2.t60.t15.t15.t7.t7.t7.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t6 t2.t60.t15.t15.t7.t7.t7.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t10 t2.t60.t15.t15.t7.t7.t7.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t6 t2.t60.t15.t15.t7.t7.t7.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t7.t14 t2.t60.t15.t15.t7.t7.t7.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t6 t2.t60.t15.t15.t7.t7.t7.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t5 t2.t60.t15.t15.t7.t7.t7.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t9.t3 t2.t60.t15.t15.t7.t7.t7.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t8 t2.t60.t15.t15.t7.t7.t7.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t7 t2.t60.t15.t15.t7.t7.t7.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t11 t2.t60.t15.t15.t7.t7.t7.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t15.t2 t2.t60.t15.t15.t7.t7.t7.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t14 t2.t60.t15.t15.t7.t7.t7.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t13 t2.t60.t15.t15.t7.t7.t7.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t4 t2.t60.t15.t15.t7.t7.t7.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t19 t2.t60.t15.t15.t7.t7.t7.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t18 t2.t60.t15.t15.t7.t7.t7.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t10.t22 t2.t60.t15.t15.t7.t7.t7.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t10.t24 t2.t60.t15.t15.t7.t7.t7.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t9 t2.t60.t15.t15.t7.t7.t7.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t7.t8 t2.t60.t15.t15.t7.t7.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t7.t5 t2.t60.t15.t15.t7.t7.t7.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t7.t4 t2.t60.t15.t15.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t16 t2.t60.t15.t15.t7.t7.t7.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t15 t2.t60.t15.t15.t7.t7.t7.t18))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t19 t2.t60.t15.t15.t7.t7.t7.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t7.t21 t2.t60.t15.t15.t7.t7.t7.t22))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t6 t2.t60.t15.t15.t7.t7.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t10.t4 t2.t60.t15.t15.t7.t7.t10.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t10.t8.t3 t2.t60.t15.t15.t7.t7.t10.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t10.t7 t2.t60.t15.t15.t7.t7.t10.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t10.t6 t2.t60.t15.t15.t7.t7.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t10.t10 t2.t60.t15.t15.t7.t7.t10.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t10.t12 t2.t60.t15.t15.t7.t7.t10.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t10.t14 t2.t60.t15.t15.t7.t7.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t10.t16 t2.t60.t15.t15.t7.t7.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t9 t2.t60.t15.t15.t7.t7.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t8 t2.t60.t15.t15.t7.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t5 t2.t60.t15.t15.t7.t7.t12 a5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t6 t2.t60.t15.t15.t7.t7.t16.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t7 t2.t60.t15.t15.t7.t7.t16.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t6 t2.t60.t15.t15.t7.t7.t16.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t10 t2.t60.t15.t15.t7.t7.t16.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t6 t2.t60.t15.t15.t7.t7.t16.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t16.t14 t2.t60.t15.t15.t7.t7.t16.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t15 t2.t60.t15.t15.t7.t7.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t5 t2.t60.t15.t15.t7.t7.t19.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t9.t3 t2.t60.t15.t15.t7.t7.t19.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t8 t2.t60.t15.t15.t7.t7.t19.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t7 t2.t60.t15.t15.t7.t7.t19.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t11 t2.t60.t15.t15.t7.t7.t19.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t15.t2 t2.t60.t15.t15.t7.t7.t19.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t14 t2.t60.t15.t15.t7.t7.t19.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t13 t2.t60.t15.t15.t7.t7.t19.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t4 t2.t60.t15.t15.t7.t7.t19.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t19 t2.t60.t15.t15.t7.t7.t19.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t18 t2.t60.t15.t15.t7.t7.t19.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t19.t22 t2.t60.t15.t15.t7.t7.t19.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t19.t24 t2.t60.t15.t15.t7.t7.t19.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t18 t2.t60.t15.t15.t7.t7.t19))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t7.t7.t17 t2.t60.t15.t15.t7.t7.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t14 t2.t60.t15.t15.t7.t7.t21 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t7.t4 t2.t60.t15.t15.t7.t7.t13 t2.t60.t15.t15.t7.t7.t22 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t7.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t25 t2.t60.t15.t15.t7.t7.t26))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t24 t2.t60.t15.t15.t7.t7.t27))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t28 t2.t60.t15.t15.t7.t7.t29))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t7.t30 t2.t60.t15.t15.t7.t7.t31))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t6 t2.t60.t15.t15.t7.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t10.t4 t2.t60.t15.t15.t7.t10.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t10.t8.t3 t2.t60.t15.t15.t7.t10.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t10.t7 t2.t60.t15.t15.t7.t10.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t10.t6 t2.t60.t15.t15.t7.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t10.t10 t2.t60.t15.t15.t7.t10.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t10.t12 t2.t60.t15.t15.t7.t10.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t10.t14 t2.t60.t15.t15.t7.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t7.t10.t16 t2.t60.t15.t15.t7.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t7.t9 t2.t60.t15.t15.t7.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t8 t2.t60.t15.t15.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t7.t5 t2.t60.t15.t15.t7.t12 a6))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t16.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t16.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t6 t2.t60.t15.t15.t7.t16.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t7 t2.t60.t15.t15.t7.t16.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t6 t2.t60.t15.t15.t7.t16.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t10 t2.t60.t15.t15.t7.t16.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t6 t2.t60.t15.t15.t7.t16.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t7.t14 t2.t60.t15.t15.t7.t16.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t6 t2.t60.t15.t15.t7.t16.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t5 t2.t60.t15.t15.t7.t16.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t9.t3 t2.t60.t15.t15.t7.t16.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t8 t2.t60.t15.t15.t7.t16.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t7 t2.t60.t15.t15.t7.t16.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t11 t2.t60.t15.t15.t7.t16.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t15.t2 t2.t60.t15.t15.t7.t16.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t14 t2.t60.t15.t15.t7.t16.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t13 t2.t60.t15.t15.t7.t16.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t4 t2.t60.t15.t15.t7.t16.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t19 t2.t60.t15.t15.t7.t16.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t18 t2.t60.t15.t15.t7.t16.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t10.t22 t2.t60.t15.t15.t7.t16.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t10.t24 t2.t60.t15.t15.t7.t16.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t9 t2.t60.t15.t15.t7.t16.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t7.t16.t8 t2.t60.t15.t15.t7.t16.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t7.t16.t5 t2.t60.t15.t15.t7.t16.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t16.t4 t2.t60.t15.t15.t7.t16.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t16.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t16.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t16 t2.t60.t15.t15.t7.t16.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t15 t2.t60.t15.t15.t7.t16.t18))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t19 t2.t60.t15.t15.t7.t16.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t16.t21 t2.t60.t15.t15.t7.t16.t22))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t15 t2.t60.t15.t15.t7.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t19.t4 t2.t60.t15.t15.t7.t19.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t19.t8.t3 t2.t60.t15.t15.t7.t19.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t19.t7 t2.t60.t15.t15.t7.t19.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t19.t6 t2.t60.t15.t15.t7.t19.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t19.t10 t2.t60.t15.t15.t7.t19.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t19.t12 t2.t60.t15.t15.t7.t19.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t19.t14 t2.t60.t15.t15.t7.t19.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t7.t19.t16 t2.t60.t15.t15.t7.t19.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t7.t18 t2.t60.t15.t15.t7.t19))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t17 t2.t60.t15.t15.t7.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t7.t14 t2.t60.t15.t15.t7.t21 a5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t25.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t7.t25.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t7.t25.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t6 t2.t60.t15.t15.t7.t25.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t7 t2.t60.t15.t15.t7.t25.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t6 t2.t60.t15.t15.t7.t25.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t10 t2.t60.t15.t15.t7.t25.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t6 t2.t60.t15.t15.t7.t25.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t25.t14 t2.t60.t15.t15.t7.t25.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t7.t24 t2.t60.t15.t15.t7.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t5 t2.t60.t15.t15.t7.t28.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t9.t3 t2.t60.t15.t15.t7.t28.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t8 t2.t60.t15.t15.t7.t28.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t7 t2.t60.t15.t15.t7.t28.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t11 t2.t60.t15.t15.t7.t28.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t15.t2 t2.t60.t15.t15.t7.t28.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t14 t2.t60.t15.t15.t7.t28.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t13 t2.t60.t15.t15.t7.t28.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t4 t2.t60.t15.t15.t7.t28.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t19 t2.t60.t15.t15.t7.t28.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t18 t2.t60.t15.t15.t7.t28.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t28.t22 t2.t60.t15.t15.t7.t28.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t7.t28.t24 t2.t60.t15.t15.t7.t28.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t7.t27 t2.t60.t15.t15.t7.t28))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t7.t26 t2.t60.t15.t15.t7.t29))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t7.t23 t2.t60.t15.t15.t7.t30 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t7.t4 t2.t60.t15.t15.t7.t13 t2.t60.t15.t15.t7.t22 t2.t60.t15.t15.t7.t31 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t15.t15.t7.t32))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t15.t15.t7.t32))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t34 t2.t60.t15.t15.t7.t35))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t36 t2.t60.t15.t15.t7.t37))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t15.t7.t33 t2.t60.t15.t15.t7.t38))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t15.t7.t34 t2.t60.t15.t15.t7.t37))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t15.t15.t7.t40 t2.t60.t15.t15.t7.t35))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t15.t15.t7.t39 t2.t60.t15.t15.t7.t41))
% 0.78/1.02 (step t2.t60.t15.t15.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t7.t42 t2.t60.t15.t15.t7.t43))
% 0.78/1.02 (step t2.t60.t15.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t6 t2.t60.t15.t15.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t15.t10.t5 t2.t60.t15.t15.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t15.t10.t7 t2.t60.t15.t15.t10.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t10.t4 t2.t60.t15.t15.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t10.t12.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t10.t12.t4 t2.t60.t15.t15.t10.t12.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t10.t12.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t15.t10.t11 t2.t60.t15.t15.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t15.t10.t10 t2.t60.t15.t15.t10.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t15.t10.t15 t2.t60.t15.t15.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t15.t10.t17 t2.t60.t15.t15.t10.t18))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t10.t14 t2.t60.t15.t15.t10.t19))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t10.t22.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t10.t22.t2 t2.t60.t15.t15.t10.t22.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t15.t15.t10.t22.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t10.t21 t2.t60.t15.t15.t10.t22))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t10.t20 t2.t60.t15.t15.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t10.t24 t2.t60.t15.t15.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t15.t10.t26 t2.t60.t15.t15.t10.t27))
% 0.78/1.02 (step t2.t60.t15.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t15.t9 t2.t60.t15.t15.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t15.t15.t8 t2.t60.t15.t15.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t15.t15.t5 t2.t60.t15.t15.t12 a7))
% 0.78/1.02 (step t2.t60.t15.t15.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t16.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t16.t7.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t6 t2.t60.t15.t15.t16.t7.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t7 t2.t60.t15.t15.t16.t7.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t6 t2.t60.t15.t15.t16.t7.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t10 t2.t60.t15.t15.t16.t7.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t6 t2.t60.t15.t15.t16.t7.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t7.t14 t2.t60.t15.t15.t16.t7.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t6 t2.t60.t15.t15.t16.t7.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t5 t2.t60.t15.t15.t16.t7.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t9.t3 t2.t60.t15.t15.t16.t7.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t8 t2.t60.t15.t15.t16.t7.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t7 t2.t60.t15.t15.t16.t7.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t11 t2.t60.t15.t15.t16.t7.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t15.t2 t2.t60.t15.t15.t16.t7.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t14 t2.t60.t15.t15.t16.t7.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t13 t2.t60.t15.t15.t16.t7.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t4 t2.t60.t15.t15.t16.t7.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t19 t2.t60.t15.t15.t16.t7.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t18 t2.t60.t15.t15.t16.t7.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t10.t22 t2.t60.t15.t15.t16.t7.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t10.t24 t2.t60.t15.t15.t16.t7.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t9 t2.t60.t15.t15.t16.t7.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t16.t7.t8 t2.t60.t15.t15.t16.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t16.t7.t5 t2.t60.t15.t15.t16.t7.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t16.t7.t4 t2.t60.t15.t15.t16.t7.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t16.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t16.t7.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t16 t2.t60.t15.t15.t16.t7.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t15 t2.t60.t15.t15.t16.t7.t18))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t19 t2.t60.t15.t15.t16.t7.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t7.t21 t2.t60.t15.t15.t16.t7.t22))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t16.t6 t2.t60.t15.t15.t16.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t10.t4 t2.t60.t15.t15.t16.t10.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t16.t10.t8.t3 t2.t60.t15.t15.t16.t10.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t10.t7 t2.t60.t15.t15.t16.t10.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t10.t6 t2.t60.t15.t15.t16.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t16.t10.t10 t2.t60.t15.t15.t16.t10.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t10.t12 t2.t60.t15.t15.t16.t10.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t10.t14 t2.t60.t15.t15.t16.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t16.t10.t16 t2.t60.t15.t15.t16.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t16.t9 t2.t60.t15.t15.t16.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t16.t8 t2.t60.t15.t15.t16.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t16.t5 t2.t60.t15.t15.t16.t12 a5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t16.t16.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t16.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t16.t16.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t6 t2.t60.t15.t15.t16.t16.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t7 t2.t60.t15.t15.t16.t16.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t6 t2.t60.t15.t15.t16.t16.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t10 t2.t60.t15.t15.t16.t16.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t6 t2.t60.t15.t15.t16.t16.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t16.t14 t2.t60.t15.t15.t16.t16.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t16.t15 t2.t60.t15.t15.t16.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t5 t2.t60.t15.t15.t16.t19.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t9.t3 t2.t60.t15.t15.t16.t19.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t8 t2.t60.t15.t15.t16.t19.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t7 t2.t60.t15.t15.t16.t19.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t11 t2.t60.t15.t15.t16.t19.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t15.t2 t2.t60.t15.t15.t16.t19.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t14 t2.t60.t15.t15.t16.t19.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t13 t2.t60.t15.t15.t16.t19.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t4 t2.t60.t15.t15.t16.t19.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t19 t2.t60.t15.t15.t16.t19.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t18 t2.t60.t15.t15.t16.t19.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t19.t22 t2.t60.t15.t15.t16.t19.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t16.t19.t24 t2.t60.t15.t15.t16.t19.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t16.t18 t2.t60.t15.t15.t16.t19))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t16.t17 t2.t60.t15.t15.t16.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t16.t14 t2.t60.t15.t15.t16.t21 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t16.t4 t2.t60.t15.t15.t16.t13 t2.t60.t15.t15.t16.t22 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t16.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t16.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t16.t25 t2.t60.t15.t15.t16.t26))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t16.t24 t2.t60.t15.t15.t16.t27))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t15.t16.t28 t2.t60.t15.t15.t16.t29))
% 0.78/1.02 (step t2.t60.t15.t15.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t16.t30 t2.t60.t15.t15.t16.t31))
% 0.78/1.02 (step t2.t60.t15.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t15 t2.t60.t15.t15.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t19.t4 t2.t60.t15.t15.t19.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t19.t8.t3 t2.t60.t15.t15.t19.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t19.t7 t2.t60.t15.t15.t19.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t19.t6 t2.t60.t15.t15.t19.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t19.t10 t2.t60.t15.t15.t19.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t15.t19.t12 t2.t60.t15.t15.t19.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t19.t14 t2.t60.t15.t15.t19.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t19.t16 t2.t60.t15.t15.t19.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t18 t2.t60.t15.t15.t19))
% 0.78/1.02 (step t2.t60.t15.t15.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t17 t2.t60.t15.t15.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t14 t2.t60.t15.t15.t21 a6))
% 0.78/1.02 (step t2.t60.t15.t15.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t25.t7.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t25.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t25.t7.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t6 t2.t60.t15.t15.t25.t7.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t7 t2.t60.t15.t15.t25.t7.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t6 t2.t60.t15.t15.t25.t7.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t10 t2.t60.t15.t15.t25.t7.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t6 t2.t60.t15.t15.t25.t7.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t25.t7.t14 t2.t60.t15.t15.t25.t7.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t25.t6 t2.t60.t15.t15.t25.t7))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t5 t2.t60.t15.t15.t25.t10.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t9.t3 t2.t60.t15.t15.t25.t10.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t8 t2.t60.t15.t15.t25.t10.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t7 t2.t60.t15.t15.t25.t10.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t11 t2.t60.t15.t15.t25.t10.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t15.t2 t2.t60.t15.t15.t25.t10.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t14 t2.t60.t15.t15.t25.t10.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t13 t2.t60.t15.t15.t25.t10.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t4 t2.t60.t15.t15.t25.t10.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t19 t2.t60.t15.t15.t25.t10.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t18 t2.t60.t15.t15.t25.t10.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t25.t10.t22 t2.t60.t15.t15.t25.t10.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t25.t10.t24 t2.t60.t15.t15.t25.t10.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t25.t9 t2.t60.t15.t15.t25.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t25.t8 t2.t60.t15.t15.t25.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t25.t5 t2.t60.t15.t15.t25.t12 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t25.t4 t2.t60.t15.t15.t25.t13 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t25.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t25.t14))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t25.t16 t2.t60.t15.t15.t25.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t25.t15 t2.t60.t15.t15.t25.t18))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t15.t25.t19 t2.t60.t15.t15.t25.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t25.t21 t2.t60.t15.t15.t25.t22))
% 0.78/1.02 (step t2.t60.t15.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t24 t2.t60.t15.t15.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t28.t4 t2.t60.t15.t15.t28.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t28.t8.t3 t2.t60.t15.t15.t28.t8.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t28.t7 t2.t60.t15.t15.t28.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t28.t6 t2.t60.t15.t15.t28.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t28.t10 t2.t60.t15.t15.t28.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t28.t12 t2.t60.t15.t15.t28.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t28.t14 t2.t60.t15.t15.t28.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t15.t28.t16 t2.t60.t15.t15.t28.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t15.t27 t2.t60.t15.t15.t28))
% 0.78/1.02 (step t2.t60.t15.t15.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t26 t2.t60.t15.t15.t29))
% 0.78/1.02 (step t2.t60.t15.t15.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t15.t23 t2.t60.t15.t15.t30 a5))
% 0.78/1.02 (step t2.t60.t15.t15.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.78/1.02 (step t2.t60.t15.t15.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t34.t4 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t34.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t15.t34.t5))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t15.t34.t6 t2.t60.t15.t15.t34.t8))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t15.t34.t7 t2.t60.t15.t15.t34.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t15.t34.t6 t2.t60.t15.t15.t34.t11))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t15.t34.t10 t2.t60.t15.t15.t34.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t15.t34.t6 t2.t60.t15.t15.t34.t13))
% 0.78/1.02 (step t2.t60.t15.t15.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t34.t14 t2.t60.t15.t15.t34.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t15.t33 t2.t60.t15.t15.t34))
% 0.78/1.02 (step t2.t60.t15.t15.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t15.t37.t5 t2.t60.t15.t15.t37.t6))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t15.t37.t9.t3 t2.t60.t15.t15.t37.t9.t4))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t37.t8 t2.t60.t15.t15.t37.t9))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t15.t37.t7 t2.t60.t15.t15.t37.t10))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t37.t11 t2.t60.t15.t15.t37.t12))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t15.t37.t15.t2 t2.t60.t15.t15.t37.t15.t3))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t37.t14 t2.t60.t15.t15.t37.t15))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t15.t37.t13 t2.t60.t15.t15.t37.t16))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t15.t37.t4 t2.t60.t15.t15.t37.t17))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t15.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t15.t37.t20.t2))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t37.t19 t2.t60.t15.t15.t37.t20))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t15.t37.t18 t2.t60.t15.t15.t37.t21))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t37.t22 t2.t60.t15.t15.t37.t23))
% 0.78/1.02 (step t2.t60.t15.t15.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t15.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t15.t37.t24 t2.t60.t15.t15.t37.t25))
% 0.78/1.02 (step t2.t60.t15.t15.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t15.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t15.t36 t2.t60.t15.t15.t37))
% 0.78/1.02 (step t2.t60.t15.t15.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t15.t35 t2.t60.t15.t15.t38))
% 0.78/1.02 (step t2.t60.t15.t15.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t15.t32 t2.t60.t15.t15.t39 a4))
% 0.78/1.02 (step t2.t60.t15.t15.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t15.t4 t2.t60.t15.t15.t13 t2.t60.t15.t15.t22 t2.t60.t15.t15.t31 t2.t60.t15.t15.t40 a3 a2 a1 a0))
% 0.78/1.02 (step t2.t60.t15.t15.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t15.t41))
% 0.78/1.02 (step t2.t60.t15.t15.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t60.t15.t15.t41))
% 0.78/1.02 (step t2.t60.t15.t15.t44 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t60.t15.t15.t43 t2.t60.t15.t15.t44))
% 0.78/1.02 (step t2.t60.t15.t15.t46 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t15.t45 t2.t60.t15.t15.t46))
% 0.78/1.02 (step t2.t60.t15.t15.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t15.t42 t2.t60.t15.t15.t47))
% 0.78/1.02 (step t2.t60.t15.t15.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t15.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t15.t48 t2.t60.t15.t15.t49))
% 0.78/1.02 (step t2.t60.t15.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.78/1.02 (step t2.t60.t15.t16 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t14 t2.t60.t15.t15))
% 0.78/1.02 (step t2.t60.t15.t17 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.78/1.02 (anchor :step t2.t60.t15.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.78/1.02 (step t2.t60.t15.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t60.t15.t18.t5 t2.t60.t15.t18.t6))
% 0.78/1.02 (step t2.t60.t15.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t18.t7 t2.t60.t15.t18.t8))
% 0.78/1.02 (step t2.t60.t15.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t18.t4 t2.t60.t15.t18.t9))
% 0.78/1.02 (step t2.t60.t15.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.78/1.02 (anchor :step t2.t60.t15.t18.t12 :args ((W $$unsorted) (:= W W)))
% 0.78/1.02 (step t2.t60.t15.t18.t12.t1 (cl (= W W)) :rule refl)
% 0.78/1.02 (step t2.t60.t15.t18.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t18.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t60.t15.t18.t12.t2))
% 0.78/1.02 (step t2.t60.t15.t18.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.78/1.02 (step t2.t60.t15.t18.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t60.t15.t18.t12.t3 t2.t60.t15.t18.t12.t4))
% 0.85/1.02 (step t2.t60.t15.t18.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t15.t18.t11 t2.t60.t15.t18.t12))
% 0.85/1.02 (step t2.t60.t15.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t15.t18.t10 t2.t60.t15.t18.t13))
% 0.85/1.02 (step t2.t60.t15.t18.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t18.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t18.t14 t2.t60.t15.t18.t15))
% 0.85/1.02 (step t2.t60.t15.t18.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t18.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t18.t16 t2.t60.t15.t18.t17))
% 0.85/1.02 (step t2.t60.t15.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t19 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t17 t2.t60.t15.t18))
% 0.85/1.02 (step t2.t60.t15.t20 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t16 t2.t60.t15.t19))
% 0.85/1.02 (step t2.t60.t15.t21 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t13 t2.t60.t15.t20 a8))
% 0.85/1.02 (step t2.t60.t15.t22 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t23 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t7.t7.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t7.t7.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t6 t2.t60.t15.t24.t7.t7.t7.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t7 t2.t60.t15.t24.t7.t7.t7.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t6 t2.t60.t15.t24.t7.t7.t7.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t10 t2.t60.t15.t24.t7.t7.t7.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t6 t2.t60.t15.t24.t7.t7.t7.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t7.t14 t2.t60.t15.t24.t7.t7.t7.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t6 t2.t60.t15.t24.t7.t7.t7))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t5 t2.t60.t15.t24.t7.t7.t10.t6))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t9.t3 t2.t60.t15.t24.t7.t7.t10.t9.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t8 t2.t60.t15.t24.t7.t7.t10.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t7 t2.t60.t15.t24.t7.t7.t10.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t11 t2.t60.t15.t24.t7.t7.t10.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t15.t2 t2.t60.t15.t24.t7.t7.t10.t15.t3))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t14 t2.t60.t15.t24.t7.t7.t10.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t13 t2.t60.t15.t24.t7.t7.t10.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t4 t2.t60.t15.t24.t7.t7.t10.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t20.t2))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t19 t2.t60.t15.t24.t7.t7.t10.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t18 t2.t60.t15.t24.t7.t7.t10.t21))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t10.t22 t2.t60.t15.t24.t7.t7.t10.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t10.t24 t2.t60.t15.t24.t7.t7.t10.t25))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t9 t2.t60.t15.t24.t7.t7.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t24.t7.t7.t8 t2.t60.t15.t24.t7.t7.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t24.t7.t7.t5 t2.t60.t15.t24.t7.t7.t12 a4))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t7.t7.t4 t2.t60.t15.t24.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t7.t7.t14))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t7.t7.t14))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t16 t2.t60.t15.t24.t7.t7.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t15 t2.t60.t15.t24.t7.t7.t18))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t19 t2.t60.t15.t24.t7.t7.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t7.t21 t2.t60.t15.t24.t7.t7.t22))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t7.t6 t2.t60.t15.t24.t7.t7))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t10.t4 t2.t60.t15.t24.t7.t10.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t7.t10.t8.t3 t2.t60.t15.t24.t7.t10.t8.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t10.t7 t2.t60.t15.t24.t7.t10.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t10.t6 t2.t60.t15.t24.t7.t10.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t7.t10.t10 t2.t60.t15.t24.t7.t10.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t10.t12 t2.t60.t15.t24.t7.t10.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t10.t14 t2.t60.t15.t24.t7.t10.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t24.t7.t10.t16 t2.t60.t15.t24.t7.t10.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t24.t7.t9 t2.t60.t15.t24.t7.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t7.t8 t2.t60.t15.t24.t7.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t24.t7.t5 t2.t60.t15.t24.t7.t12 a5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t7.t16.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t7.t16.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t6 t2.t60.t15.t24.t7.t16.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t7 t2.t60.t15.t24.t7.t16.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t6 t2.t60.t15.t24.t7.t16.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t10 t2.t60.t15.t24.t7.t16.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t6 t2.t60.t15.t24.t7.t16.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t16.t14 t2.t60.t15.t24.t7.t16.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t7.t15 t2.t60.t15.t24.t7.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t5 t2.t60.t15.t24.t7.t19.t6))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t9.t3 t2.t60.t15.t24.t7.t19.t9.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t8 t2.t60.t15.t24.t7.t19.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t7 t2.t60.t15.t24.t7.t19.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t11 t2.t60.t15.t24.t7.t19.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t15.t2 t2.t60.t15.t24.t7.t19.t15.t3))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t14 t2.t60.t15.t24.t7.t19.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t13 t2.t60.t15.t24.t7.t19.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t4 t2.t60.t15.t24.t7.t19.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t20.t2))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t19 t2.t60.t15.t24.t7.t19.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t18 t2.t60.t15.t24.t7.t19.t21))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t19.t22 t2.t60.t15.t24.t7.t19.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t7.t19.t24 t2.t60.t15.t24.t7.t19.t25))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t24.t7.t18 t2.t60.t15.t24.t7.t19))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t24.t7.t17 t2.t60.t15.t24.t7.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t24.t7.t14 t2.t60.t15.t24.t7.t21 a4))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t7.t4 t2.t60.t15.t24.t7.t13 t2.t60.t15.t24.t7.t22 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t7.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t7.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t7.t25 t2.t60.t15.t24.t7.t26))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t24.t7.t24 t2.t60.t15.t24.t7.t27))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t24.t7.t28 t2.t60.t15.t24.t7.t29))
% 0.85/1.02 (step t2.t60.t15.t24.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t7.t30 t2.t60.t15.t24.t7.t31))
% 0.85/1.02 (step t2.t60.t15.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t6 t2.t60.t15.t24.t7))
% 0.85/1.02 (step t2.t60.t15.t24.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t10.t4 t2.t60.t15.t24.t10.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t10.t8.t3 t2.t60.t15.t24.t10.t8.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t10.t7 t2.t60.t15.t24.t10.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t10.t6 t2.t60.t15.t24.t10.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t10.t10 t2.t60.t15.t24.t10.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t24.t10.t12 t2.t60.t15.t24.t10.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t10.t14 t2.t60.t15.t24.t10.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t24.t10.t16 t2.t60.t15.t24.t10.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t24.t9 t2.t60.t15.t24.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t8 t2.t60.t15.t24.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t24.t5 t2.t60.t15.t24.t12 a6))
% 0.85/1.02 (step t2.t60.t15.t24.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t16.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t16.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t6 t2.t60.t15.t24.t16.t7.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t7 t2.t60.t15.t24.t16.t7.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t6 t2.t60.t15.t24.t16.t7.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t10 t2.t60.t15.t24.t16.t7.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t6 t2.t60.t15.t24.t16.t7.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t16.t7.t14 t2.t60.t15.t24.t16.t7.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t16.t6 t2.t60.t15.t24.t16.t7))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t5 t2.t60.t15.t24.t16.t10.t6))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t9.t3 t2.t60.t15.t24.t16.t10.t9.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t8 t2.t60.t15.t24.t16.t10.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t7 t2.t60.t15.t24.t16.t10.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t11 t2.t60.t15.t24.t16.t10.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t15.t2 t2.t60.t15.t24.t16.t10.t15.t3))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t14 t2.t60.t15.t24.t16.t10.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t13 t2.t60.t15.t24.t16.t10.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t4 t2.t60.t15.t24.t16.t10.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t20.t2))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t19 t2.t60.t15.t24.t16.t10.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t18 t2.t60.t15.t24.t16.t10.t21))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t16.t10.t22 t2.t60.t15.t24.t16.t10.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t16.t10.t24 t2.t60.t15.t24.t16.t10.t25))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t24.t16.t9 t2.t60.t15.t24.t16.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t24.t16.t8 t2.t60.t15.t24.t16.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t24.t16.t5 t2.t60.t15.t24.t16.t12 a4))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t16.t4 t2.t60.t15.t24.t16.t13 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t16.t14))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t16.t14))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t16.t16 t2.t60.t15.t24.t16.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t16.t15 t2.t60.t15.t24.t16.t18))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t24.t16.t19 t2.t60.t15.t24.t16.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t16.t21 t2.t60.t15.t24.t16.t22))
% 0.85/1.02 (step t2.t60.t15.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t15 t2.t60.t15.t24.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t19.t4 t2.t60.t15.t24.t19.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t19.t8.t3 t2.t60.t15.t24.t19.t8.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t19.t7 t2.t60.t15.t24.t19.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t19.t6 t2.t60.t15.t24.t19.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t19.t10 t2.t60.t15.t24.t19.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t19.t12 t2.t60.t15.t24.t19.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t19.t14 t2.t60.t15.t24.t19.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t24.t19.t16 t2.t60.t15.t24.t19.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t24.t18 t2.t60.t15.t24.t19))
% 0.85/1.02 (step t2.t60.t15.t24.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t17 t2.t60.t15.t24.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t24.t14 t2.t60.t15.t24.t21 a5))
% 0.85/1.02 (step t2.t60.t15.t24.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t24.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t25.t4 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t24.t25.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t24.t25.t5))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t24.t25.t6 t2.t60.t15.t24.t25.t8))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t24.t25.t7 t2.t60.t15.t24.t25.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t24.t25.t6 t2.t60.t15.t24.t25.t11))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t24.t25.t10 t2.t60.t15.t24.t25.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t24.t25.t6 t2.t60.t15.t24.t25.t13))
% 0.85/1.02 (step t2.t60.t15.t24.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t25.t14 t2.t60.t15.t24.t25.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t24.t24 t2.t60.t15.t24.t25))
% 0.85/1.02 (step t2.t60.t15.t24.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t24.t28.t5 t2.t60.t15.t24.t28.t6))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t24.t28.t9.t3 t2.t60.t15.t24.t28.t9.t4))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t28.t8 t2.t60.t15.t24.t28.t9))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t24.t28.t7 t2.t60.t15.t24.t28.t10))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t28.t11 t2.t60.t15.t24.t28.t12))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t24.t28.t15.t2 t2.t60.t15.t24.t28.t15.t3))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t28.t14 t2.t60.t15.t24.t28.t15))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t24.t28.t13 t2.t60.t15.t24.t28.t16))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t24.t28.t4 t2.t60.t15.t24.t28.t17))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t24.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t24.t28.t20.t2))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t28.t19 t2.t60.t15.t24.t28.t20))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t24.t28.t18 t2.t60.t15.t24.t28.t21))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t28.t22 t2.t60.t15.t24.t28.t23))
% 0.85/1.02 (step t2.t60.t15.t24.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t24.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t24.t28.t24 t2.t60.t15.t24.t28.t25))
% 0.85/1.02 (step t2.t60.t15.t24.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t24.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t24.t27 t2.t60.t15.t24.t28))
% 0.85/1.02 (step t2.t60.t15.t24.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t24.t26 t2.t60.t15.t24.t29))
% 0.85/1.02 (step t2.t60.t15.t24.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t24.t23 t2.t60.t15.t24.t30 a4))
% 0.85/1.02 (step t2.t60.t15.t24.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t24.t4 t2.t60.t15.t24.t13 t2.t60.t15.t24.t22 t2.t60.t15.t24.t31 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t24.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t15.t24.t32))
% 0.85/1.02 (step t2.t60.t15.t24.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t15.t24.t32))
% 0.85/1.02 (step t2.t60.t15.t24.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t24.t34 t2.t60.t15.t24.t35))
% 0.85/1.02 (step t2.t60.t15.t24.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t15.t24.t36 t2.t60.t15.t24.t37))
% 0.85/1.02 (step t2.t60.t15.t24.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t15.t24.t33 t2.t60.t15.t24.t38))
% 0.85/1.02 (step t2.t60.t15.t24.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t24.t34 t2.t60.t15.t24.t37))
% 0.85/1.02 (step t2.t60.t15.t24.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t15.t24.t40 t2.t60.t15.t24.t35))
% 0.85/1.02 (step t2.t60.t15.t24.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t15.t24.t39 t2.t60.t15.t24.t41))
% 0.85/1.02 (step t2.t60.t15.t24.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t24.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t24.t42 t2.t60.t15.t24.t43))
% 0.85/1.02 (step t2.t60.t15.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t25 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t23 t2.t60.t15.t24))
% 0.85/1.02 (step t2.t60.t15.t26 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t15.t27.t5 t2.t60.t15.t27.t6))
% 0.85/1.02 (step t2.t60.t15.t27.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t27.t7 t2.t60.t15.t27.t8))
% 0.85/1.02 (step t2.t60.t15.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t27.t4 t2.t60.t15.t27.t9))
% 0.85/1.02 (step t2.t60.t15.t27.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t27.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t27.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t27.t12.t3))
% 0.85/1.02 (step t2.t60.t15.t27.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t27.t12.t4 t2.t60.t15.t27.t12.t5))
% 0.85/1.02 (step t2.t60.t15.t27.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t27.t12.t6))
% 0.85/1.02 (step t2.t60.t15.t27.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t27.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t27.t11 t2.t60.t15.t27.t12))
% 0.85/1.02 (step t2.t60.t15.t27.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t27.t10 t2.t60.t15.t27.t13))
% 0.85/1.02 (step t2.t60.t15.t27.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t15.t27.t15 t2.t60.t15.t27.t16))
% 0.85/1.02 (step t2.t60.t15.t27.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t15.t27.t17 t2.t60.t15.t27.t18))
% 0.85/1.02 (step t2.t60.t15.t27.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t27.t14 t2.t60.t15.t27.t19))
% 0.85/1.02 (step t2.t60.t15.t27.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.02 (anchor :step t2.t60.t15.t27.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t27.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t27.t22.t3))
% 0.85/1.02 (step t2.t60.t15.t27.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t27.t22.t2 t2.t60.t15.t27.t22.t4))
% 0.85/1.02 (step t2.t60.t15.t27.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t15.t27.t22.t5))
% 0.85/1.02 (step t2.t60.t15.t27.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t27.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t27.t21 t2.t60.t15.t27.t22))
% 0.85/1.02 (step t2.t60.t15.t27.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t27.t20 t2.t60.t15.t27.t23))
% 0.85/1.02 (step t2.t60.t15.t27.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t27.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t27.t24 t2.t60.t15.t27.t25))
% 0.85/1.02 (step t2.t60.t15.t27.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t27.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t15.t27.t26 t2.t60.t15.t27.t27))
% 0.85/1.02 (step t2.t60.t15.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t28 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t15.t26 t2.t60.t15.t27))
% 0.85/1.02 (step t2.t60.t15.t29 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t15.t25 t2.t60.t15.t28))
% 0.85/1.02 (step t2.t60.t15.t30 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t15.t22 t2.t60.t15.t29 a7))
% 0.85/1.02 (step t2.t60.t15.t31 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t32 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t33.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t33.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t33.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t33.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t33.t7.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t33.t7.t7.t5))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t6 t2.t60.t15.t33.t7.t7.t8))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t7 t2.t60.t15.t33.t7.t7.t9))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t6 t2.t60.t15.t33.t7.t7.t11))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t10 t2.t60.t15.t33.t7.t7.t12))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t6 t2.t60.t15.t33.t7.t7.t13))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t7.t7.t14 t2.t60.t15.t33.t7.t7.t15))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t33.t7.t6 t2.t60.t15.t33.t7.t7))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.02 (anchor :step t2.t60.t15.t33.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t5 t2.t60.t15.t33.t7.t10.t6))
% 0.85/1.02 (step t2.t60.t15.t33.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t9.t3 t2.t60.t15.t33.t7.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t8 t2.t60.t15.t33.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t7 t2.t60.t15.t33.t7.t10.t10))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t11 t2.t60.t15.t33.t7.t10.t12))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t15.t2 t2.t60.t15.t33.t7.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t14 t2.t60.t15.t33.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t13 t2.t60.t15.t33.t7.t10.t16))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t4 t2.t60.t15.t33.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t19 t2.t60.t15.t33.t7.t10.t20))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t18 t2.t60.t15.t33.t7.t10.t21))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t7.t10.t22 t2.t60.t15.t33.t7.t10.t23))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t33.t7.t10.t24 t2.t60.t15.t33.t7.t10.t25))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t33.t7.t9 t2.t60.t15.t33.t7.t10))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t33.t7.t8 t2.t60.t15.t33.t7.t11))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t33.t7.t5 t2.t60.t15.t33.t7.t12 a4))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t33.t7.t4 t2.t60.t15.t33.t7.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t33.t7.t14))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t33.t7.t14))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t33.t7.t16 t2.t60.t15.t33.t7.t17))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t33.t7.t15 t2.t60.t15.t33.t7.t18))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t33.t7.t19 t2.t60.t15.t33.t7.t20))
% 0.85/1.03 (step t2.t60.t15.t33.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t7.t21 t2.t60.t15.t33.t7.t22))
% 0.85/1.03 (step t2.t60.t15.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t33.t6 t2.t60.t15.t33.t7))
% 0.85/1.03 (step t2.t60.t15.t33.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t33.t10.t4 t2.t60.t15.t33.t10.t5))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t33.t10.t8.t3 t2.t60.t15.t33.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t10.t7 t2.t60.t15.t33.t10.t8))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t10.t6 t2.t60.t15.t33.t10.t9))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t33.t10.t10 t2.t60.t15.t33.t10.t11))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t10.t12 t2.t60.t15.t33.t10.t13))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t10.t14 t2.t60.t15.t33.t10.t15))
% 0.85/1.03 (step t2.t60.t15.t33.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t33.t10.t16 t2.t60.t15.t33.t10.t17))
% 0.85/1.03 (step t2.t60.t15.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t33.t9 t2.t60.t15.t33.t10))
% 0.85/1.03 (step t2.t60.t15.t33.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t33.t8 t2.t60.t15.t33.t11))
% 0.85/1.03 (step t2.t60.t15.t33.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t33.t5 t2.t60.t15.t33.t12 a5))
% 0.85/1.03 (step t2.t60.t15.t33.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t15.t33.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t33.t16.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t33.t16.t5))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t33.t16.t5))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t33.t16.t6 t2.t60.t15.t33.t16.t8))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t33.t16.t7 t2.t60.t15.t33.t16.t9))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t33.t16.t6 t2.t60.t15.t33.t16.t11))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t33.t16.t10 t2.t60.t15.t33.t16.t12))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t33.t16.t6 t2.t60.t15.t33.t16.t13))
% 0.85/1.03 (step t2.t60.t15.t33.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t16.t14 t2.t60.t15.t33.t16.t15))
% 0.85/1.03 (step t2.t60.t15.t33.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t33.t15 t2.t60.t15.t33.t16))
% 0.85/1.03 (step t2.t60.t15.t33.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t33.t19.t5 t2.t60.t15.t33.t19.t6))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t33.t19.t9.t3 t2.t60.t15.t33.t19.t9.t4))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t19.t8 t2.t60.t15.t33.t19.t9))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t33.t19.t7 t2.t60.t15.t33.t19.t10))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t33.t19.t11 t2.t60.t15.t33.t19.t12))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t33.t19.t15.t2 t2.t60.t15.t33.t19.t15.t3))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t33.t19.t14 t2.t60.t15.t33.t19.t15))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t33.t19.t13 t2.t60.t15.t33.t19.t16))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t33.t19.t4 t2.t60.t15.t33.t19.t17))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t33.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t33.t19.t20.t2))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t33.t19.t19 t2.t60.t15.t33.t19.t20))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t33.t19.t18 t2.t60.t15.t33.t19.t21))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t19.t22 t2.t60.t15.t33.t19.t23))
% 0.85/1.03 (step t2.t60.t15.t33.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t33.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t33.t19.t24 t2.t60.t15.t33.t19.t25))
% 0.85/1.03 (step t2.t60.t15.t33.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t33.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t33.t18 t2.t60.t15.t33.t19))
% 0.85/1.03 (step t2.t60.t15.t33.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t33.t17 t2.t60.t15.t33.t20))
% 0.85/1.03 (step t2.t60.t15.t33.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t33.t14 t2.t60.t15.t33.t21 a4))
% 0.85/1.03 (step t2.t60.t15.t33.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t33.t4 t2.t60.t15.t33.t13 t2.t60.t15.t33.t22 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t33.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t33.t23))
% 0.85/1.03 (step t2.t60.t15.t33.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t33.t23))
% 0.85/1.03 (step t2.t60.t15.t33.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t33.t25 t2.t60.t15.t33.t26))
% 0.85/1.03 (step t2.t60.t15.t33.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t33.t24 t2.t60.t15.t33.t27))
% 0.85/1.03 (step t2.t60.t15.t33.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t15.t33.t28 t2.t60.t15.t33.t29))
% 0.85/1.03 (step t2.t60.t15.t33.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t33.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t33.t30 t2.t60.t15.t33.t31))
% 0.85/1.03 (step t2.t60.t15.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t34 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t32 t2.t60.t15.t33))
% 0.85/1.03 (step t2.t60.t15.t35 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t36.t4 t2.t60.t15.t36.t5))
% 0.85/1.03 (step t2.t60.t15.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t36.t8.t3 t2.t60.t15.t36.t8.t4))
% 0.85/1.03 (step t2.t60.t15.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t36.t7 t2.t60.t15.t36.t8))
% 0.85/1.03 (step t2.t60.t15.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t36.t6 t2.t60.t15.t36.t9))
% 0.85/1.03 (step t2.t60.t15.t36.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t15.t36.t10 t2.t60.t15.t36.t11))
% 0.85/1.03 (step t2.t60.t15.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t15.t36.t12 t2.t60.t15.t36.t13))
% 0.85/1.03 (step t2.t60.t15.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t36.t14 t2.t60.t15.t36.t15))
% 0.85/1.03 (step t2.t60.t15.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t36.t16 t2.t60.t15.t36.t17))
% 0.85/1.03 (step t2.t60.t15.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t37 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t35 t2.t60.t15.t36))
% 0.85/1.03 (step t2.t60.t15.t38 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t34 t2.t60.t15.t37))
% 0.85/1.03 (step t2.t60.t15.t39 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t31 t2.t60.t15.t38 a6))
% 0.85/1.03 (step t2.t60.t15.t40 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t15.t41 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t15.t42.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t15.t42.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t42.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t42.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t42.t7.t5))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t42.t7.t5))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t42.t7.t6 t2.t60.t15.t42.t7.t8))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t42.t7.t7 t2.t60.t15.t42.t7.t9))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t42.t7.t6 t2.t60.t15.t42.t7.t11))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t42.t7.t10 t2.t60.t15.t42.t7.t12))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t42.t7.t6 t2.t60.t15.t42.t7.t13))
% 0.85/1.03 (step t2.t60.t15.t42.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t42.t7.t14 t2.t60.t15.t42.t7.t15))
% 0.85/1.03 (step t2.t60.t15.t42.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t42.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t42.t6 t2.t60.t15.t42.t7))
% 0.85/1.03 (step t2.t60.t15.t42.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t42.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t42.t10.t5 t2.t60.t15.t42.t10.t6))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t42.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t42.t10.t9.t3 t2.t60.t15.t42.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t42.t10.t8 t2.t60.t15.t42.t10.t9))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t42.t10.t7 t2.t60.t15.t42.t10.t10))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t42.t10.t11 t2.t60.t15.t42.t10.t12))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t42.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t42.t10.t15.t2 t2.t60.t15.t42.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t42.t10.t14 t2.t60.t15.t42.t10.t15))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t42.t10.t13 t2.t60.t15.t42.t10.t16))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t42.t10.t4 t2.t60.t15.t42.t10.t17))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t42.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t42.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t42.t10.t19 t2.t60.t15.t42.t10.t20))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t42.t10.t18 t2.t60.t15.t42.t10.t21))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t42.t10.t22 t2.t60.t15.t42.t10.t23))
% 0.85/1.03 (step t2.t60.t15.t42.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t42.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t42.t10.t24 t2.t60.t15.t42.t10.t25))
% 0.85/1.03 (step t2.t60.t15.t42.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t42.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t42.t9 t2.t60.t15.t42.t10))
% 0.85/1.03 (step t2.t60.t15.t42.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t42.t8 t2.t60.t15.t42.t11))
% 0.85/1.03 (step t2.t60.t15.t42.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t42.t5 t2.t60.t15.t42.t12 a4))
% 0.85/1.03 (step t2.t60.t15.t42.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t42.t4 t2.t60.t15.t42.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t42.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t42.t14))
% 0.85/1.03 (step t2.t60.t15.t42.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t42.t14))
% 0.85/1.03 (step t2.t60.t15.t42.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t42.t16 t2.t60.t15.t42.t17))
% 0.85/1.03 (step t2.t60.t15.t42.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t42.t15 t2.t60.t15.t42.t18))
% 0.85/1.03 (step t2.t60.t15.t42.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t15.t42.t19 t2.t60.t15.t42.t20))
% 0.85/1.03 (step t2.t60.t15.t42.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t42.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t42.t21 t2.t60.t15.t42.t22))
% 0.85/1.03 (step t2.t60.t15.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t43 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t41 t2.t60.t15.t42))
% 0.85/1.03 (step t2.t60.t15.t44 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t45.t4 t2.t60.t15.t45.t5))
% 0.85/1.03 (step t2.t60.t15.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t45.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t45.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t45.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t45.t8.t3 t2.t60.t15.t45.t8.t4))
% 0.85/1.03 (step t2.t60.t15.t45.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t45.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t45.t7 t2.t60.t15.t45.t8))
% 0.85/1.03 (step t2.t60.t15.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t45.t6 t2.t60.t15.t45.t9))
% 0.85/1.03 (step t2.t60.t15.t45.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t15.t45.t10 t2.t60.t15.t45.t11))
% 0.85/1.03 (step t2.t60.t15.t45.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t45.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t45.t12 t2.t60.t15.t45.t13))
% 0.85/1.03 (step t2.t60.t15.t45.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t45.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t45.t14 t2.t60.t15.t45.t15))
% 0.85/1.03 (step t2.t60.t15.t45.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t45.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t15.t45.t16 t2.t60.t15.t45.t17))
% 0.85/1.03 (step t2.t60.t15.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t46 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t44 t2.t60.t15.t45))
% 0.85/1.03 (step t2.t60.t15.t47 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t43 t2.t60.t15.t46))
% 0.85/1.03 (step t2.t60.t15.t48 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t15.t40 t2.t60.t15.t47 a5))
% 0.85/1.03 (step t2.t60.t15.t49 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t15.t50 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t51 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t51.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t15.t51.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t51.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t51.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t51.t5))
% 0.85/1.03 (step t2.t60.t15.t51.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t15.t51.t5))
% 0.85/1.03 (step t2.t60.t15.t51.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t15.t51.t6 t2.t60.t15.t51.t8))
% 0.85/1.03 (step t2.t60.t15.t51.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t15.t51.t7 t2.t60.t15.t51.t9))
% 0.85/1.03 (step t2.t60.t15.t51.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t15.t51.t6 t2.t60.t15.t51.t11))
% 0.85/1.03 (step t2.t60.t15.t51.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t15.t51.t10 t2.t60.t15.t51.t12))
% 0.85/1.03 (step t2.t60.t15.t51.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t15.t51.t6 t2.t60.t15.t51.t13))
% 0.85/1.03 (step t2.t60.t15.t51.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t51.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t51.t14 t2.t60.t15.t51.t15))
% 0.85/1.03 (step t2.t60.t15.t51 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t52 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t50 t2.t60.t15.t51))
% 0.85/1.03 (step t2.t60.t15.t53 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t15.t54 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t54.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t15.t54.t5 t2.t60.t15.t54.t6))
% 0.85/1.03 (step t2.t60.t15.t54.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t54.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t54.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t15.t54.t9.t3 t2.t60.t15.t54.t9.t4))
% 0.85/1.03 (step t2.t60.t15.t54.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t54.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t54.t8 t2.t60.t15.t54.t9))
% 0.85/1.03 (step t2.t60.t15.t54.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t15.t54.t7 t2.t60.t15.t54.t10))
% 0.85/1.03 (step t2.t60.t15.t54.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t54.t11 t2.t60.t15.t54.t12))
% 0.85/1.03 (step t2.t60.t15.t54.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t54.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t54.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t15.t54.t15.t2 t2.t60.t15.t54.t15.t3))
% 0.85/1.03 (step t2.t60.t15.t54.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t54.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t54.t14 t2.t60.t15.t54.t15))
% 0.85/1.03 (step t2.t60.t15.t54.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t15.t54.t13 t2.t60.t15.t54.t16))
% 0.85/1.03 (step t2.t60.t15.t54.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t15.t54.t4 t2.t60.t15.t54.t17))
% 0.85/1.03 (step t2.t60.t15.t54.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t15.t54.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t15.t54.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t15.t54.t20.t2))
% 0.85/1.03 (step t2.t60.t15.t54.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t54.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t54.t19 t2.t60.t15.t54.t20))
% 0.85/1.03 (step t2.t60.t15.t54.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t15.t54.t18 t2.t60.t15.t54.t21))
% 0.85/1.03 (step t2.t60.t15.t54.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t54.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t54.t22 t2.t60.t15.t54.t23))
% 0.85/1.03 (step t2.t60.t15.t54.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t15.t54.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t15.t54.t24 t2.t60.t15.t54.t25))
% 0.85/1.03 (step t2.t60.t15.t54 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t55 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t15.t53 t2.t60.t15.t54))
% 0.85/1.03 (step t2.t60.t15.t56 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t15.t52 t2.t60.t15.t55))
% 0.85/1.03 (step t2.t60.t15.t57 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t15.t49 t2.t60.t15.t56 a4))
% 0.85/1.03 (step t2.t60.t15.t58 (cl (and (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t15.t3 t2.t60.t15.t12 a10 a9 t2.t60.t15.t21 t2.t60.t15.t30 t2.t60.t15.t39 t2.t60.t15.t48 t2.t60.t15.t57 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t15.t59 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t15.t58))
% 0.85/1.03 (step t2.t60.t15.t60 (cl (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule and :premises (t2.t60.t15.t58))
% 0.85/1.03 (anchor :step t2.t60.t15.t61 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t15.t61.t1 (cl (= P P)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t61.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t61.t3 (cl (= (@ Phi P) (@ Phi P))) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t61.t4 (cl (= (@ tptp.mnot (@ Phi P)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)))) :rule cong :premises (t2.t60.t15.t59 t2.t60.t15.t61.t3))
% 0.85/1.03 (step t2.t60.t15.t61.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t61.t6 (cl (= (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t61.t4 t2.t60.t15.t61.t5))
% 0.85/1.03 (step t2.t60.t15.t61 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t15.t62 (cl (= (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))))) :rule cong :premises (t2.t60.t15.t60 t2.t60.t15.t61))
% 0.85/1.03 (step t2.t60.t15.t63 (cl (= (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))))) :rule cong :premises (t2.t60.t15.t59 t2.t60.t15.t62))
% 0.85/1.03 (step t2.t60.t15.t64 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t15.t65 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t60.t15.t63 t2.t60.t15.t64))
% 0.85/1.03 (step t2.t60.t15 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t16 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t60.t14 t2.t60.t15))
% 0.85/1.03 (step t2.t60.t17 (cl (= tptp.mexists_prop tptp.mexists_prop)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t18 :args ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t4 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t18.t5 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t18.t5.t1 (cl (= P P)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))) __flatten_var_0))) :rule cong :premises (t2.t60.t18.t5.t3 t2.t60.t18.t5.t4))
% 0.85/1.03 (step t2.t60.t18.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))) __flatten_var_0) (not (@ (@ Phi P) __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0) (not (@ (@ Phi P) __flatten_var_0)))) :rule trans :premises (t2.t60.t18.t5.t5 t2.t60.t18.t5.t6))
% 0.85/1.03 (step t2.t60.t18.t5 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t18.t6 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))))) :rule cong :premises (t2.t60.t18.t4 t2.t60.t18.t5))
% 0.85/1.03 (step t2.t60.t18.t7 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t18.t8 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t18.t8.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t18.t8.t2 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.85/1.03 (step t2.t60.t18.t8.t2.t1 (cl (= P P)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t8.t2.t2 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t8.t2.t4 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) W))) :rule cong :premises (t2.t60.t18.t8.t2.t2 t2.t60.t18.t8.t2.t3))
% 0.85/1.03 (step t2.t60.t18.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) W) (not (@ (@ Phi P) W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t8.t2.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W) (not (@ (@ Phi P) W)))) :rule trans :premises (t2.t60.t18.t8.t2.t4 t2.t60.t18.t8.t2.t5))
% 0.85/1.03 (step t2.t60.t18.t8.t2 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t18.t8 (cl (= (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t18.t9 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule trans :premises (t2.t60.t18.t7 t2.t60.t18.t8))
% 0.85/1.03 (step t2.t60.t18.t10 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule trans :premises (t2.t60.t18.t6 t2.t60.t18.t9))
% 0.85/1.03 (step t2.t60.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule cong :premises (t2.t60.t18.t3 t2.t60.t18.t10))
% 0.85/1.03 (step t2.t60.t18.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t18.t13 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t18.t13.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule cong :premises (t2.t60.t18.t13.t2))
% 0.85/1.03 (step t2.t60.t18.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule trans :premises (t2.t60.t18.t12 t2.t60.t18.t13))
% 0.85/1.03 (step t2.t60.t18.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule trans :premises (t2.t60.t18.t11 t2.t60.t18.t14))
% 0.85/1.03 (step t2.t60.t18.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t18.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t18.t15 t2.t60.t18.t16))
% 0.85/1.03 (step t2.t60.t18.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) __flatten_var_0) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t18.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) :rule trans :premises (t2.t60.t18.t17 t2.t60.t18.t18))
% 0.85/1.03 (step t2.t60.t18 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t19 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) :rule cong :premises (t2.t60.t17 t2.t60.t18))
% 0.85/1.03 (step t2.t60.t20 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) :rule trans :premises (t2.t60.t16 t2.t60.t19))
% 0.85/1.03 (step t2.t60.t21 (cl (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule resolution :premises (t2.t60.t13 t2.t60.t20 a12))
% 0.85/1.03 (step t2.t60.t22 (cl (not (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t23 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t3 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t4 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t5 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t6 t2.t60.t24.t6.t7.t7.t7.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t7 t2.t60.t24.t6.t7.t7.t7.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t6 t2.t60.t24.t6.t7.t7.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t10 t2.t60.t24.t6.t7.t7.t7.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t6 t2.t60.t24.t6.t7.t7.t7.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t7.t14 t2.t60.t24.t6.t7.t7.t7.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t6 t2.t60.t24.t6.t7.t7.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t5 t2.t60.t24.t6.t7.t7.t7.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t9.t3 t2.t60.t24.t6.t7.t7.t7.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t8 t2.t60.t24.t6.t7.t7.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t7 t2.t60.t24.t6.t7.t7.t7.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t11 t2.t60.t24.t6.t7.t7.t7.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t15.t2 t2.t60.t24.t6.t7.t7.t7.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t14 t2.t60.t24.t6.t7.t7.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t13 t2.t60.t24.t6.t7.t7.t7.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t4 t2.t60.t24.t6.t7.t7.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t19 t2.t60.t24.t6.t7.t7.t7.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t18 t2.t60.t24.t6.t7.t7.t7.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t10.t22 t2.t60.t24.t6.t7.t7.t7.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t10.t24 t2.t60.t24.t6.t7.t7.t7.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t9 t2.t60.t24.t6.t7.t7.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t7.t8 t2.t60.t24.t6.t7.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t7.t5 t2.t60.t24.t6.t7.t7.t7.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t7.t4 t2.t60.t24.t6.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t16 t2.t60.t24.t6.t7.t7.t7.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t15 t2.t60.t24.t6.t7.t7.t7.t18))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t19 t2.t60.t24.t6.t7.t7.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t7.t21 t2.t60.t24.t6.t7.t7.t7.t22))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t6 t2.t60.t24.t6.t7.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t10.t4 t2.t60.t24.t6.t7.t7.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t10.t8.t3 t2.t60.t24.t6.t7.t7.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t10.t7 t2.t60.t24.t6.t7.t7.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t10.t6 t2.t60.t24.t6.t7.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t10.t10 t2.t60.t24.t6.t7.t7.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t10.t12 t2.t60.t24.t6.t7.t7.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t10.t14 t2.t60.t24.t6.t7.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t10.t16 t2.t60.t24.t6.t7.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t9 t2.t60.t24.t6.t7.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t8 t2.t60.t24.t6.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t5 t2.t60.t24.t6.t7.t7.t12 a5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t6 t2.t60.t24.t6.t7.t7.t16.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t7 t2.t60.t24.t6.t7.t7.t16.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t6 t2.t60.t24.t6.t7.t7.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t10 t2.t60.t24.t6.t7.t7.t16.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t6 t2.t60.t24.t6.t7.t7.t16.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t16.t14 t2.t60.t24.t6.t7.t7.t16.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t15 t2.t60.t24.t6.t7.t7.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t5 t2.t60.t24.t6.t7.t7.t19.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t9.t3 t2.t60.t24.t6.t7.t7.t19.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t8 t2.t60.t24.t6.t7.t7.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t7 t2.t60.t24.t6.t7.t7.t19.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t11 t2.t60.t24.t6.t7.t7.t19.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t15.t2 t2.t60.t24.t6.t7.t7.t19.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t14 t2.t60.t24.t6.t7.t7.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t13 t2.t60.t24.t6.t7.t7.t19.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t4 t2.t60.t24.t6.t7.t7.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t19 t2.t60.t24.t6.t7.t7.t19.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t18 t2.t60.t24.t6.t7.t7.t19.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t19.t22 t2.t60.t24.t6.t7.t7.t19.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t19.t24 t2.t60.t24.t6.t7.t7.t19.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t18 t2.t60.t24.t6.t7.t7.t19))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t7.t7.t17 t2.t60.t24.t6.t7.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t14 t2.t60.t24.t6.t7.t7.t21 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t7.t4 t2.t60.t24.t6.t7.t7.t13 t2.t60.t24.t6.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t7.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t25 t2.t60.t24.t6.t7.t7.t26))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t24 t2.t60.t24.t6.t7.t7.t27))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t28 t2.t60.t24.t6.t7.t7.t29))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t7.t30 t2.t60.t24.t6.t7.t7.t31))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t6 t2.t60.t24.t6.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t10.t4 t2.t60.t24.t6.t7.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t10.t8.t3 t2.t60.t24.t6.t7.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t10.t7 t2.t60.t24.t6.t7.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t10.t6 t2.t60.t24.t6.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t10.t10 t2.t60.t24.t6.t7.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t10.t12 t2.t60.t24.t6.t7.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t10.t14 t2.t60.t24.t6.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t7.t10.t16 t2.t60.t24.t6.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t7.t9 t2.t60.t24.t6.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t8 t2.t60.t24.t6.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t7.t5 t2.t60.t24.t6.t7.t12 a6))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t16.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t16.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t6 t2.t60.t24.t6.t7.t16.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t7 t2.t60.t24.t6.t7.t16.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t6 t2.t60.t24.t6.t7.t16.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t10 t2.t60.t24.t6.t7.t16.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t6 t2.t60.t24.t6.t7.t16.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t7.t14 t2.t60.t24.t6.t7.t16.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t6 t2.t60.t24.t6.t7.t16.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t5 t2.t60.t24.t6.t7.t16.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t9.t3 t2.t60.t24.t6.t7.t16.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t8 t2.t60.t24.t6.t7.t16.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t7 t2.t60.t24.t6.t7.t16.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t11 t2.t60.t24.t6.t7.t16.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t15.t2 t2.t60.t24.t6.t7.t16.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t14 t2.t60.t24.t6.t7.t16.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t13 t2.t60.t24.t6.t7.t16.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t4 t2.t60.t24.t6.t7.t16.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t19 t2.t60.t24.t6.t7.t16.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t18 t2.t60.t24.t6.t7.t16.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t10.t22 t2.t60.t24.t6.t7.t16.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t10.t24 t2.t60.t24.t6.t7.t16.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t9 t2.t60.t24.t6.t7.t16.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t7.t16.t8 t2.t60.t24.t6.t7.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t7.t16.t5 t2.t60.t24.t6.t7.t16.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t16.t4 t2.t60.t24.t6.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t16.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t16.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t16 t2.t60.t24.t6.t7.t16.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t15 t2.t60.t24.t6.t7.t16.t18))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t19 t2.t60.t24.t6.t7.t16.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t16.t21 t2.t60.t24.t6.t7.t16.t22))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t15 t2.t60.t24.t6.t7.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t19.t4 t2.t60.t24.t6.t7.t19.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t19.t8.t3 t2.t60.t24.t6.t7.t19.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t19.t7 t2.t60.t24.t6.t7.t19.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t19.t6 t2.t60.t24.t6.t7.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t19.t10 t2.t60.t24.t6.t7.t19.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t19.t12 t2.t60.t24.t6.t7.t19.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t19.t14 t2.t60.t24.t6.t7.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t7.t19.t16 t2.t60.t24.t6.t7.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t7.t18 t2.t60.t24.t6.t7.t19))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t17 t2.t60.t24.t6.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t7.t14 t2.t60.t24.t6.t7.t21 a5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t7.t25.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t7.t25.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t6 t2.t60.t24.t6.t7.t25.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t7 t2.t60.t24.t6.t7.t25.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t6 t2.t60.t24.t6.t7.t25.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t10 t2.t60.t24.t6.t7.t25.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t6 t2.t60.t24.t6.t7.t25.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t25.t14 t2.t60.t24.t6.t7.t25.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t7.t24 t2.t60.t24.t6.t7.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t5 t2.t60.t24.t6.t7.t28.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t9.t3 t2.t60.t24.t6.t7.t28.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t8 t2.t60.t24.t6.t7.t28.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t7 t2.t60.t24.t6.t7.t28.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t11 t2.t60.t24.t6.t7.t28.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t15.t2 t2.t60.t24.t6.t7.t28.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t14 t2.t60.t24.t6.t7.t28.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t13 t2.t60.t24.t6.t7.t28.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t4 t2.t60.t24.t6.t7.t28.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t19 t2.t60.t24.t6.t7.t28.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t18 t2.t60.t24.t6.t7.t28.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t28.t22 t2.t60.t24.t6.t7.t28.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t7.t28.t24 t2.t60.t24.t6.t7.t28.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t7.t27 t2.t60.t24.t6.t7.t28))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t7.t26 t2.t60.t24.t6.t7.t29))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t7.t23 t2.t60.t24.t6.t7.t30 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t7.t4 t2.t60.t24.t6.t7.t13 t2.t60.t24.t6.t7.t22 t2.t60.t24.t6.t7.t31 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t24.t6.t7.t32))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t24.t6.t7.t32))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t34 t2.t60.t24.t6.t7.t35))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t36 t2.t60.t24.t6.t7.t37))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t24.t6.t7.t33 t2.t60.t24.t6.t7.t38))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t24.t6.t7.t34 t2.t60.t24.t6.t7.t37))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t24.t6.t7.t40 t2.t60.t24.t6.t7.t35))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t24.t6.t7.t39 t2.t60.t24.t6.t7.t41))
% 0.85/1.03 (step t2.t60.t24.t6.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t7.t42 t2.t60.t24.t6.t7.t43))
% 0.85/1.03 (step t2.t60.t24.t6.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t6 t2.t60.t24.t6.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t24.t6.t10.t5 t2.t60.t24.t6.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t24.t6.t10.t7 t2.t60.t24.t6.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t10.t4 t2.t60.t24.t6.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t10.t12.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t10.t12.t4 t2.t60.t24.t6.t10.t12.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t10.t12.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t6.t10.t11 t2.t60.t24.t6.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t6.t10.t10 t2.t60.t24.t6.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t24.t6.t10.t15 t2.t60.t24.t6.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t24.t6.t10.t17 t2.t60.t24.t6.t10.t18))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t10.t14 t2.t60.t24.t6.t10.t19))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t10.t22.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t10.t22.t2 t2.t60.t24.t6.t10.t22.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t24.t6.t10.t22.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t10.t21 t2.t60.t24.t6.t10.t22))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t10.t20 t2.t60.t24.t6.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t10.t24 t2.t60.t24.t6.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t6.t10.t26 t2.t60.t24.t6.t10.t27))
% 0.85/1.03 (step t2.t60.t24.t6.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t24.t6.t9 t2.t60.t24.t6.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t24.t6.t8 t2.t60.t24.t6.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t24.t6.t5 t2.t60.t24.t6.t12 a7))
% 0.85/1.03 (step t2.t60.t24.t6.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t16.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t16.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t6 t2.t60.t24.t6.t16.t7.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t7 t2.t60.t24.t6.t16.t7.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t6 t2.t60.t24.t6.t16.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t10 t2.t60.t24.t6.t16.t7.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t6 t2.t60.t24.t6.t16.t7.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t7.t14 t2.t60.t24.t6.t16.t7.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t6 t2.t60.t24.t6.t16.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t5 t2.t60.t24.t6.t16.t7.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t9.t3 t2.t60.t24.t6.t16.t7.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t8 t2.t60.t24.t6.t16.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t7 t2.t60.t24.t6.t16.t7.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t11 t2.t60.t24.t6.t16.t7.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t15.t2 t2.t60.t24.t6.t16.t7.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t14 t2.t60.t24.t6.t16.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t13 t2.t60.t24.t6.t16.t7.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t4 t2.t60.t24.t6.t16.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t19 t2.t60.t24.t6.t16.t7.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t18 t2.t60.t24.t6.t16.t7.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t10.t22 t2.t60.t24.t6.t16.t7.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t10.t24 t2.t60.t24.t6.t16.t7.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t9 t2.t60.t24.t6.t16.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t16.t7.t8 t2.t60.t24.t6.t16.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t16.t7.t5 t2.t60.t24.t6.t16.t7.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t16.t7.t4 t2.t60.t24.t6.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t16.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t16.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t16 t2.t60.t24.t6.t16.t7.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t15 t2.t60.t24.t6.t16.t7.t18))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t19 t2.t60.t24.t6.t16.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t7.t21 t2.t60.t24.t6.t16.t7.t22))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t16.t6 t2.t60.t24.t6.t16.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t10.t4 t2.t60.t24.t6.t16.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t16.t10.t8.t3 t2.t60.t24.t6.t16.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t10.t7 t2.t60.t24.t6.t16.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t10.t6 t2.t60.t24.t6.t16.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t16.t10.t10 t2.t60.t24.t6.t16.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t10.t12 t2.t60.t24.t6.t16.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t10.t14 t2.t60.t24.t6.t16.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t16.t10.t16 t2.t60.t24.t6.t16.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t16.t9 t2.t60.t24.t6.t16.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t16.t8 t2.t60.t24.t6.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t16.t5 t2.t60.t24.t6.t16.t12 a5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t16.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t16.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t6 t2.t60.t24.t6.t16.t16.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t7 t2.t60.t24.t6.t16.t16.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t6 t2.t60.t24.t6.t16.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t10 t2.t60.t24.t6.t16.t16.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t6 t2.t60.t24.t6.t16.t16.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t16.t14 t2.t60.t24.t6.t16.t16.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t16.t15 t2.t60.t24.t6.t16.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t5 t2.t60.t24.t6.t16.t19.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t9.t3 t2.t60.t24.t6.t16.t19.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t8 t2.t60.t24.t6.t16.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t7 t2.t60.t24.t6.t16.t19.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t11 t2.t60.t24.t6.t16.t19.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t15.t2 t2.t60.t24.t6.t16.t19.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t14 t2.t60.t24.t6.t16.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t13 t2.t60.t24.t6.t16.t19.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t4 t2.t60.t24.t6.t16.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t19 t2.t60.t24.t6.t16.t19.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t18 t2.t60.t24.t6.t16.t19.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t19.t22 t2.t60.t24.t6.t16.t19.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t16.t19.t24 t2.t60.t24.t6.t16.t19.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t16.t18 t2.t60.t24.t6.t16.t19))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t16.t17 t2.t60.t24.t6.t16.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t16.t14 t2.t60.t24.t6.t16.t21 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t16.t4 t2.t60.t24.t6.t16.t13 t2.t60.t24.t6.t16.t22 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t16.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t16.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t16.t25 t2.t60.t24.t6.t16.t26))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t16.t24 t2.t60.t24.t6.t16.t27))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t24.t6.t16.t28 t2.t60.t24.t6.t16.t29))
% 0.85/1.03 (step t2.t60.t24.t6.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t16.t30 t2.t60.t24.t6.t16.t31))
% 0.85/1.03 (step t2.t60.t24.t6.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t15 t2.t60.t24.t6.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t19.t4 t2.t60.t24.t6.t19.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t19.t8.t3 t2.t60.t24.t6.t19.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t19.t7 t2.t60.t24.t6.t19.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t19.t6 t2.t60.t24.t6.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t19.t10 t2.t60.t24.t6.t19.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t24.t6.t19.t12 t2.t60.t24.t6.t19.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t19.t14 t2.t60.t24.t6.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t19.t16 t2.t60.t24.t6.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t18 t2.t60.t24.t6.t19))
% 0.85/1.03 (step t2.t60.t24.t6.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t17 t2.t60.t24.t6.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t14 t2.t60.t24.t6.t21 a6))
% 0.85/1.03 (step t2.t60.t24.t6.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t25.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t25.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t6 t2.t60.t24.t6.t25.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t7 t2.t60.t24.t6.t25.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t6 t2.t60.t24.t6.t25.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t10 t2.t60.t24.t6.t25.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t6 t2.t60.t24.t6.t25.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t25.t7.t14 t2.t60.t24.t6.t25.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t25.t6 t2.t60.t24.t6.t25.t7))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t5 t2.t60.t24.t6.t25.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t9.t3 t2.t60.t24.t6.t25.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t8 t2.t60.t24.t6.t25.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t7 t2.t60.t24.t6.t25.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t11 t2.t60.t24.t6.t25.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t15.t2 t2.t60.t24.t6.t25.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t14 t2.t60.t24.t6.t25.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t13 t2.t60.t24.t6.t25.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t4 t2.t60.t24.t6.t25.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t19 t2.t60.t24.t6.t25.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t18 t2.t60.t24.t6.t25.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t25.t10.t22 t2.t60.t24.t6.t25.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t25.t10.t24 t2.t60.t24.t6.t25.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t25.t9 t2.t60.t24.t6.t25.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t25.t8 t2.t60.t24.t6.t25.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t25.t5 t2.t60.t24.t6.t25.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t25.t4 t2.t60.t24.t6.t25.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t25.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t25.t14))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t25.t16 t2.t60.t24.t6.t25.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t25.t15 t2.t60.t24.t6.t25.t18))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t6.t25.t19 t2.t60.t24.t6.t25.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t25.t21 t2.t60.t24.t6.t25.t22))
% 0.85/1.03 (step t2.t60.t24.t6.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t24 t2.t60.t24.t6.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t28.t4 t2.t60.t24.t6.t28.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t28.t8.t3 t2.t60.t24.t6.t28.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t28.t7 t2.t60.t24.t6.t28.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t28.t6 t2.t60.t24.t6.t28.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t28.t10 t2.t60.t24.t6.t28.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t28.t12 t2.t60.t24.t6.t28.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t28.t14 t2.t60.t24.t6.t28.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t6.t28.t16 t2.t60.t24.t6.t28.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t6.t27 t2.t60.t24.t6.t28))
% 0.85/1.03 (step t2.t60.t24.t6.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t26 t2.t60.t24.t6.t29))
% 0.85/1.03 (step t2.t60.t24.t6.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t6.t23 t2.t60.t24.t6.t30 a5))
% 0.85/1.03 (step t2.t60.t24.t6.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t6.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t34.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t34.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t6.t34.t5))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t6.t34.t6 t2.t60.t24.t6.t34.t8))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t6.t34.t7 t2.t60.t24.t6.t34.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t6.t34.t6 t2.t60.t24.t6.t34.t11))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t6.t34.t10 t2.t60.t24.t6.t34.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t6.t34.t6 t2.t60.t24.t6.t34.t13))
% 0.85/1.03 (step t2.t60.t24.t6.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t34.t14 t2.t60.t24.t6.t34.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t6.t33 t2.t60.t24.t6.t34))
% 0.85/1.03 (step t2.t60.t24.t6.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t6.t37.t5 t2.t60.t24.t6.t37.t6))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t6.t37.t9.t3 t2.t60.t24.t6.t37.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t37.t8 t2.t60.t24.t6.t37.t9))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t6.t37.t7 t2.t60.t24.t6.t37.t10))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t37.t11 t2.t60.t24.t6.t37.t12))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t6.t37.t15.t2 t2.t60.t24.t6.t37.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t37.t14 t2.t60.t24.t6.t37.t15))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t6.t37.t13 t2.t60.t24.t6.t37.t16))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t6.t37.t4 t2.t60.t24.t6.t37.t17))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t6.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t6.t37.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t37.t19 t2.t60.t24.t6.t37.t20))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t6.t37.t18 t2.t60.t24.t6.t37.t21))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t37.t22 t2.t60.t24.t6.t37.t23))
% 0.85/1.03 (step t2.t60.t24.t6.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t6.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t6.t37.t24 t2.t60.t24.t6.t37.t25))
% 0.85/1.03 (step t2.t60.t24.t6.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t6.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t6.t36 t2.t60.t24.t6.t37))
% 0.85/1.03 (step t2.t60.t24.t6.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t6.t35 t2.t60.t24.t6.t38))
% 0.85/1.03 (step t2.t60.t24.t6.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t6.t32 t2.t60.t24.t6.t39 a4))
% 0.85/1.03 (step t2.t60.t24.t6.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t6.t4 t2.t60.t24.t6.t13 t2.t60.t24.t6.t22 t2.t60.t24.t6.t31 t2.t60.t24.t6.t40 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t6.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t6.t41))
% 0.85/1.03 (step t2.t60.t24.t6.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t60.t24.t6.t41))
% 0.85/1.03 (step t2.t60.t24.t6.t44 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t60.t24.t6.t43 t2.t60.t24.t6.t44))
% 0.85/1.03 (step t2.t60.t24.t6.t46 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t60.t24.t6.t45 t2.t60.t24.t6.t46))
% 0.85/1.03 (step t2.t60.t24.t6.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t60.t24.t6.t42 t2.t60.t24.t6.t47))
% 0.85/1.03 (step t2.t60.t24.t6.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t6.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t6.t48 t2.t60.t24.t6.t49))
% 0.85/1.03 (step t2.t60.t24.t6 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t7 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t5 t2.t60.t24.t6))
% 0.85/1.03 (step t2.t60.t24.t8 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t9 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t9.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t60.t24.t9.t5 t2.t60.t24.t9.t6))
% 0.85/1.03 (step t2.t60.t24.t9.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t9.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t9.t7 t2.t60.t24.t9.t8))
% 0.85/1.03 (step t2.t60.t24.t9.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t24.t9.t4 t2.t60.t24.t9.t9))
% 0.85/1.03 (step t2.t60.t24.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t9.t12 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t9.t12.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t9.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t60.t24.t9.t12.t2))
% 0.85/1.03 (step t2.t60.t24.t9.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t9.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t60.t24.t9.t12.t3 t2.t60.t24.t9.t12.t4))
% 0.85/1.03 (step t2.t60.t24.t9.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t9.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t24.t9.t11 t2.t60.t24.t9.t12))
% 0.85/1.03 (step t2.t60.t24.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t24.t9.t10 t2.t60.t24.t9.t13))
% 0.85/1.03 (step t2.t60.t24.t9.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t9.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t9.t14 t2.t60.t24.t9.t15))
% 0.85/1.03 (step t2.t60.t24.t9.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t9.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t9.t16 t2.t60.t24.t9.t17))
% 0.85/1.03 (step t2.t60.t24.t9 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t10 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t8 t2.t60.t24.t9))
% 0.85/1.03 (step t2.t60.t24.t11 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t7 t2.t60.t24.t10))
% 0.85/1.03 (step t2.t60.t24.t12 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t4 t2.t60.t24.t11 a8))
% 0.85/1.03 (step t2.t60.t24.t13 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t14 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t7.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t7.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t6 t2.t60.t24.t15.t7.t7.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t7 t2.t60.t24.t15.t7.t7.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t6 t2.t60.t24.t15.t7.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t10 t2.t60.t24.t15.t7.t7.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t6 t2.t60.t24.t15.t7.t7.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t7.t14 t2.t60.t24.t15.t7.t7.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t6 t2.t60.t24.t15.t7.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t5 t2.t60.t24.t15.t7.t7.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t9.t3 t2.t60.t24.t15.t7.t7.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t8 t2.t60.t24.t15.t7.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t7 t2.t60.t24.t15.t7.t7.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t11 t2.t60.t24.t15.t7.t7.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t15.t2 t2.t60.t24.t15.t7.t7.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t14 t2.t60.t24.t15.t7.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t13 t2.t60.t24.t15.t7.t7.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t4 t2.t60.t24.t15.t7.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t19 t2.t60.t24.t15.t7.t7.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t18 t2.t60.t24.t15.t7.t7.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t10.t22 t2.t60.t24.t15.t7.t7.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t10.t24 t2.t60.t24.t15.t7.t7.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t9 t2.t60.t24.t15.t7.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t15.t7.t7.t8 t2.t60.t24.t15.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t15.t7.t7.t5 t2.t60.t24.t15.t7.t7.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t7.t7.t4 t2.t60.t24.t15.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t7.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t7.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t16 t2.t60.t24.t15.t7.t7.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t15 t2.t60.t24.t15.t7.t7.t18))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t19 t2.t60.t24.t15.t7.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t7.t21 t2.t60.t24.t15.t7.t7.t22))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t7.t6 t2.t60.t24.t15.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t10.t4 t2.t60.t24.t15.t7.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t7.t10.t8.t3 t2.t60.t24.t15.t7.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t10.t7 t2.t60.t24.t15.t7.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t10.t6 t2.t60.t24.t15.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t7.t10.t10 t2.t60.t24.t15.t7.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t10.t12 t2.t60.t24.t15.t7.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t10.t14 t2.t60.t24.t15.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t15.t7.t10.t16 t2.t60.t24.t15.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t15.t7.t9 t2.t60.t24.t15.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t7.t8 t2.t60.t24.t15.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t15.t7.t5 t2.t60.t24.t15.t7.t12 a5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t7.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t7.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t6 t2.t60.t24.t15.t7.t16.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t7 t2.t60.t24.t15.t7.t16.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t6 t2.t60.t24.t15.t7.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t10 t2.t60.t24.t15.t7.t16.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t6 t2.t60.t24.t15.t7.t16.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t16.t14 t2.t60.t24.t15.t7.t16.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t7.t15 t2.t60.t24.t15.t7.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t5 t2.t60.t24.t15.t7.t19.t6))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t9.t3 t2.t60.t24.t15.t7.t19.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t8 t2.t60.t24.t15.t7.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t7 t2.t60.t24.t15.t7.t19.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t11 t2.t60.t24.t15.t7.t19.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t15.t2 t2.t60.t24.t15.t7.t19.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t14 t2.t60.t24.t15.t7.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t13 t2.t60.t24.t15.t7.t19.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t4 t2.t60.t24.t15.t7.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t19 t2.t60.t24.t15.t7.t19.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t18 t2.t60.t24.t15.t7.t19.t21))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t19.t22 t2.t60.t24.t15.t7.t19.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t7.t19.t24 t2.t60.t24.t15.t7.t19.t25))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t15.t7.t18 t2.t60.t24.t15.t7.t19))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t15.t7.t17 t2.t60.t24.t15.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t15.t7.t14 t2.t60.t24.t15.t7.t21 a4))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t7.t4 t2.t60.t24.t15.t7.t13 t2.t60.t24.t15.t7.t22 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t7.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t7.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t7.t25 t2.t60.t24.t15.t7.t26))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t15.t7.t24 t2.t60.t24.t15.t7.t27))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t24.t15.t7.t28 t2.t60.t24.t15.t7.t29))
% 0.85/1.03 (step t2.t60.t24.t15.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t7.t30 t2.t60.t24.t15.t7.t31))
% 0.85/1.03 (step t2.t60.t24.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t6 t2.t60.t24.t15.t7))
% 0.85/1.03 (step t2.t60.t24.t15.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t10.t4 t2.t60.t24.t15.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t10.t8.t3 t2.t60.t24.t15.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t10.t7 t2.t60.t24.t15.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t10.t6 t2.t60.t24.t15.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t10.t10 t2.t60.t24.t15.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t24.t15.t10.t12 t2.t60.t24.t15.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t10.t14 t2.t60.t24.t15.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t15.t10.t16 t2.t60.t24.t15.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t15.t9 t2.t60.t24.t15.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t8 t2.t60.t24.t15.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t15.t5 t2.t60.t24.t15.t12 a6))
% 0.85/1.03 (step t2.t60.t24.t15.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t16.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t16.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t6 t2.t60.t24.t15.t16.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t7 t2.t60.t24.t15.t16.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t6 t2.t60.t24.t15.t16.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t10 t2.t60.t24.t15.t16.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t6 t2.t60.t24.t15.t16.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t16.t7.t14 t2.t60.t24.t15.t16.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t16.t6 t2.t60.t24.t15.t16.t7))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t5 t2.t60.t24.t15.t16.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t9.t3 t2.t60.t24.t15.t16.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t8 t2.t60.t24.t15.t16.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t7 t2.t60.t24.t15.t16.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t11 t2.t60.t24.t15.t16.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t15.t2 t2.t60.t24.t15.t16.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t14 t2.t60.t24.t15.t16.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t13 t2.t60.t24.t15.t16.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t4 t2.t60.t24.t15.t16.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t19 t2.t60.t24.t15.t16.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t18 t2.t60.t24.t15.t16.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t16.t10.t22 t2.t60.t24.t15.t16.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t16.t10.t24 t2.t60.t24.t15.t16.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t15.t16.t9 t2.t60.t24.t15.t16.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t15.t16.t8 t2.t60.t24.t15.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t15.t16.t5 t2.t60.t24.t15.t16.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t16.t4 t2.t60.t24.t15.t16.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t16.t14))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t16.t14))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t16.t16 t2.t60.t24.t15.t16.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t16.t15 t2.t60.t24.t15.t16.t18))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t15.t16.t19 t2.t60.t24.t15.t16.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t16.t21 t2.t60.t24.t15.t16.t22))
% 0.85/1.03 (step t2.t60.t24.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t15 t2.t60.t24.t15.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t19.t4 t2.t60.t24.t15.t19.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t19.t8.t3 t2.t60.t24.t15.t19.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t19.t7 t2.t60.t24.t15.t19.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t19.t6 t2.t60.t24.t15.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t19.t10 t2.t60.t24.t15.t19.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t19.t12 t2.t60.t24.t15.t19.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t19.t14 t2.t60.t24.t15.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t15.t19.t16 t2.t60.t24.t15.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t15.t18 t2.t60.t24.t15.t19))
% 0.85/1.03 (step t2.t60.t24.t15.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t17 t2.t60.t24.t15.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t15.t14 t2.t60.t24.t15.t21 a5))
% 0.85/1.03 (step t2.t60.t24.t15.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t15.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t25.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t15.t25.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t15.t25.t5))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t15.t25.t6 t2.t60.t24.t15.t25.t8))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t15.t25.t7 t2.t60.t24.t15.t25.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t15.t25.t6 t2.t60.t24.t15.t25.t11))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t15.t25.t10 t2.t60.t24.t15.t25.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t15.t25.t6 t2.t60.t24.t15.t25.t13))
% 0.85/1.03 (step t2.t60.t24.t15.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t25.t14 t2.t60.t24.t15.t25.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t15.t24 t2.t60.t24.t15.t25))
% 0.85/1.03 (step t2.t60.t24.t15.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t15.t28.t5 t2.t60.t24.t15.t28.t6))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t15.t28.t9.t3 t2.t60.t24.t15.t28.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t28.t8 t2.t60.t24.t15.t28.t9))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t15.t28.t7 t2.t60.t24.t15.t28.t10))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t28.t11 t2.t60.t24.t15.t28.t12))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t15.t28.t15.t2 t2.t60.t24.t15.t28.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t28.t14 t2.t60.t24.t15.t28.t15))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t15.t28.t13 t2.t60.t24.t15.t28.t16))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t15.t28.t4 t2.t60.t24.t15.t28.t17))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t15.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t15.t28.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t28.t19 t2.t60.t24.t15.t28.t20))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t15.t28.t18 t2.t60.t24.t15.t28.t21))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t28.t22 t2.t60.t24.t15.t28.t23))
% 0.85/1.03 (step t2.t60.t24.t15.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t15.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t15.t28.t24 t2.t60.t24.t15.t28.t25))
% 0.85/1.03 (step t2.t60.t24.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t15.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t15.t27 t2.t60.t24.t15.t28))
% 0.85/1.03 (step t2.t60.t24.t15.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t15.t26 t2.t60.t24.t15.t29))
% 0.85/1.03 (step t2.t60.t24.t15.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t15.t23 t2.t60.t24.t15.t30 a4))
% 0.85/1.03 (step t2.t60.t24.t15.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t15.t4 t2.t60.t24.t15.t13 t2.t60.t24.t15.t22 t2.t60.t24.t15.t31 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t15.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t24.t15.t32))
% 0.85/1.03 (step t2.t60.t24.t15.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t24.t15.t32))
% 0.85/1.03 (step t2.t60.t24.t15.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t24.t15.t34 t2.t60.t24.t15.t35))
% 0.85/1.03 (step t2.t60.t24.t15.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t24.t15.t36 t2.t60.t24.t15.t37))
% 0.85/1.03 (step t2.t60.t24.t15.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t24.t15.t33 t2.t60.t24.t15.t38))
% 0.85/1.03 (step t2.t60.t24.t15.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t24.t15.t34 t2.t60.t24.t15.t37))
% 0.85/1.03 (step t2.t60.t24.t15.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t24.t15.t40 t2.t60.t24.t15.t35))
% 0.85/1.03 (step t2.t60.t24.t15.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t24.t15.t39 t2.t60.t24.t15.t41))
% 0.85/1.03 (step t2.t60.t24.t15.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t15.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t15.t42 t2.t60.t24.t15.t43))
% 0.85/1.03 (step t2.t60.t24.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t16 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t14 t2.t60.t24.t15))
% 0.85/1.03 (step t2.t60.t24.t17 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t24.t18.t5 t2.t60.t24.t18.t6))
% 0.85/1.03 (step t2.t60.t24.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t24.t18.t7 t2.t60.t24.t18.t8))
% 0.85/1.03 (step t2.t60.t24.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t18.t4 t2.t60.t24.t18.t9))
% 0.85/1.03 (step t2.t60.t24.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t18.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t18.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t18.t12.t3))
% 0.85/1.03 (step t2.t60.t24.t18.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t18.t12.t4 t2.t60.t24.t18.t12.t5))
% 0.85/1.03 (step t2.t60.t24.t18.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t18.t12.t6))
% 0.85/1.03 (step t2.t60.t24.t18.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t18.t11 t2.t60.t24.t18.t12))
% 0.85/1.03 (step t2.t60.t24.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t18.t10 t2.t60.t24.t18.t13))
% 0.85/1.03 (step t2.t60.t24.t18.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t24.t18.t15 t2.t60.t24.t18.t16))
% 0.85/1.03 (step t2.t60.t24.t18.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t24.t18.t17 t2.t60.t24.t18.t18))
% 0.85/1.03 (step t2.t60.t24.t18.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t18.t14 t2.t60.t24.t18.t19))
% 0.85/1.03 (step t2.t60.t24.t18.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t18.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t18.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t18.t22.t3))
% 0.85/1.03 (step t2.t60.t24.t18.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t18.t22.t2 t2.t60.t24.t18.t22.t4))
% 0.85/1.03 (step t2.t60.t24.t18.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t24.t18.t22.t5))
% 0.85/1.03 (step t2.t60.t24.t18.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t18.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t18.t21 t2.t60.t24.t18.t22))
% 0.85/1.03 (step t2.t60.t24.t18.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t18.t20 t2.t60.t24.t18.t23))
% 0.85/1.03 (step t2.t60.t24.t18.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t18.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t18.t24 t2.t60.t24.t18.t25))
% 0.85/1.03 (step t2.t60.t24.t18.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t18.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t24.t18.t26 t2.t60.t24.t18.t27))
% 0.85/1.03 (step t2.t60.t24.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t19 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t24.t17 t2.t60.t24.t18))
% 0.85/1.03 (step t2.t60.t24.t20 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t24.t16 t2.t60.t24.t19))
% 0.85/1.03 (step t2.t60.t24.t21 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t24.t13 t2.t60.t24.t20 a7))
% 0.85/1.03 (step t2.t60.t24.t22 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t23 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t24.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t24.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t24.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t24.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t24.t7.t7.t5))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t6 t2.t60.t24.t24.t7.t7.t8))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t7 t2.t60.t24.t24.t7.t7.t9))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t6 t2.t60.t24.t24.t7.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t10 t2.t60.t24.t24.t7.t7.t12))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t6 t2.t60.t24.t24.t7.t7.t13))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t7.t7.t14 t2.t60.t24.t24.t7.t7.t15))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t24.t7.t6 t2.t60.t24.t24.t7.t7))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t5 t2.t60.t24.t24.t7.t10.t6))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t9.t3 t2.t60.t24.t24.t7.t10.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t8 t2.t60.t24.t24.t7.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t7 t2.t60.t24.t24.t7.t10.t10))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t11 t2.t60.t24.t24.t7.t10.t12))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t15.t2 t2.t60.t24.t24.t7.t10.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t14 t2.t60.t24.t24.t7.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t13 t2.t60.t24.t24.t7.t10.t16))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t4 t2.t60.t24.t24.t7.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t19 t2.t60.t24.t24.t7.t10.t20))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t18 t2.t60.t24.t24.t7.t10.t21))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t7.t10.t22 t2.t60.t24.t24.t7.t10.t23))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t24.t7.t10.t24 t2.t60.t24.t24.t7.t10.t25))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t24.t7.t9 t2.t60.t24.t24.t7.t10))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t24.t7.t8 t2.t60.t24.t24.t7.t11))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t24.t7.t5 t2.t60.t24.t24.t7.t12 a4))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t24.t7.t4 t2.t60.t24.t24.t7.t13 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t24.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t24.t7.t14))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t24.t7.t16 t2.t60.t24.t24.t7.t17))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t24.t7.t15 t2.t60.t24.t24.t7.t18))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t24.t7.t19 t2.t60.t24.t24.t7.t20))
% 0.85/1.03 (step t2.t60.t24.t24.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t7.t21 t2.t60.t24.t24.t7.t22))
% 0.85/1.03 (step t2.t60.t24.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t24.t6 t2.t60.t24.t24.t7))
% 0.85/1.03 (step t2.t60.t24.t24.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t24.t10.t4 t2.t60.t24.t24.t10.t5))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t24.t10.t8.t3 t2.t60.t24.t24.t10.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t10.t7 t2.t60.t24.t24.t10.t8))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t10.t6 t2.t60.t24.t24.t10.t9))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t24.t10.t10 t2.t60.t24.t24.t10.t11))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t10.t12 t2.t60.t24.t24.t10.t13))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t10.t14 t2.t60.t24.t24.t10.t15))
% 0.85/1.03 (step t2.t60.t24.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t24.t10.t16 t2.t60.t24.t24.t10.t17))
% 0.85/1.03 (step t2.t60.t24.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t24.t9 t2.t60.t24.t24.t10))
% 0.85/1.03 (step t2.t60.t24.t24.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t24.t8 t2.t60.t24.t24.t11))
% 0.85/1.03 (step t2.t60.t24.t24.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t24.t5 t2.t60.t24.t24.t12 a5))
% 0.85/1.03 (step t2.t60.t24.t24.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.03 (step t2.t60.t24.t24.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t24.t16.t4 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t24.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t24.t16.t5))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t24.t16.t6 t2.t60.t24.t24.t16.t8))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t24.t16.t7 t2.t60.t24.t24.t16.t9))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t24.t16.t6 t2.t60.t24.t24.t16.t11))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t24.t16.t10 t2.t60.t24.t24.t16.t12))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t24.t16.t6 t2.t60.t24.t24.t16.t13))
% 0.85/1.03 (step t2.t60.t24.t24.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t16.t14 t2.t60.t24.t24.t16.t15))
% 0.85/1.03 (step t2.t60.t24.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t24.t15 t2.t60.t24.t24.t16))
% 0.85/1.03 (step t2.t60.t24.t24.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t24.t19.t5 t2.t60.t24.t24.t19.t6))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t24.t19.t9.t3 t2.t60.t24.t24.t19.t9.t4))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t19.t8 t2.t60.t24.t24.t19.t9))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t24.t19.t7 t2.t60.t24.t24.t19.t10))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t24.t19.t11 t2.t60.t24.t24.t19.t12))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t24.t19.t15.t2 t2.t60.t24.t24.t19.t15.t3))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t24.t19.t14 t2.t60.t24.t24.t19.t15))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t24.t19.t13 t2.t60.t24.t24.t19.t16))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t24.t19.t4 t2.t60.t24.t24.t19.t17))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t24.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t24.t19.t20.t2))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t24.t19.t19 t2.t60.t24.t24.t19.t20))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t24.t19.t18 t2.t60.t24.t24.t19.t21))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t19.t22 t2.t60.t24.t24.t19.t23))
% 0.85/1.03 (step t2.t60.t24.t24.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t24.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t24.t19.t24 t2.t60.t24.t24.t19.t25))
% 0.85/1.03 (step t2.t60.t24.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t24.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t24.t18 t2.t60.t24.t24.t19))
% 0.85/1.03 (step t2.t60.t24.t24.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t24.t17 t2.t60.t24.t24.t20))
% 0.85/1.03 (step t2.t60.t24.t24.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t24.t14 t2.t60.t24.t24.t21 a4))
% 0.85/1.03 (step t2.t60.t24.t24.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t24.t4 t2.t60.t24.t24.t13 t2.t60.t24.t24.t22 a3 a2 a1 a0))
% 0.85/1.03 (step t2.t60.t24.t24.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t24.t23))
% 0.85/1.03 (step t2.t60.t24.t24.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t24.t23))
% 0.85/1.03 (step t2.t60.t24.t24.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t24.t25 t2.t60.t24.t24.t26))
% 0.85/1.03 (step t2.t60.t24.t24.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t24.t24 t2.t60.t24.t24.t27))
% 0.85/1.03 (step t2.t60.t24.t24.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t24.t24.t28 t2.t60.t24.t24.t29))
% 0.85/1.03 (step t2.t60.t24.t24.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t24.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t24.t30 t2.t60.t24.t24.t31))
% 0.85/1.03 (step t2.t60.t24.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t25 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t23 t2.t60.t24.t24))
% 0.85/1.03 (step t2.t60.t24.t26 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.03 (anchor :step t2.t60.t24.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.03 (step t2.t60.t24.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t27.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t27.t4 t2.t60.t24.t27.t5))
% 0.85/1.03 (step t2.t60.t24.t27.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.03 (anchor :step t2.t60.t24.t27.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.03 (step t2.t60.t24.t27.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t27.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t27.t8.t3 t2.t60.t24.t27.t8.t4))
% 0.85/1.03 (step t2.t60.t24.t27.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t27.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t27.t7 t2.t60.t24.t27.t8))
% 0.85/1.03 (step t2.t60.t24.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t27.t6 t2.t60.t24.t27.t9))
% 0.85/1.03 (step t2.t60.t24.t27.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t24.t27.t10 t2.t60.t24.t27.t11))
% 0.85/1.03 (step t2.t60.t24.t27.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t27.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t24.t27.t12 t2.t60.t24.t27.t13))
% 0.85/1.03 (step t2.t60.t24.t27.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.03 (step t2.t60.t24.t27.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t27.t14 t2.t60.t24.t27.t15))
% 0.85/1.03 (step t2.t60.t24.t27.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.03 (step t2.t60.t24.t27.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t27.t16 t2.t60.t24.t27.t17))
% 0.85/1.03 (step t2.t60.t24.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.03 (step t2.t60.t24.t28 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t26 t2.t60.t24.t27))
% 0.85/1.04 (step t2.t60.t24.t29 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t25 t2.t60.t24.t28))
% 0.85/1.04 (step t2.t60.t24.t30 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t22 t2.t60.t24.t29 a6))
% 0.85/1.04 (step t2.t60.t24.t31 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t24.t32 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t24.t33.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t24.t33.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t33.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t33.t7.t5))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t33.t7.t5))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t33.t7.t6 t2.t60.t24.t33.t7.t8))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t33.t7.t7 t2.t60.t24.t33.t7.t9))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t33.t7.t6 t2.t60.t24.t33.t7.t11))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t33.t7.t10 t2.t60.t24.t33.t7.t12))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t33.t7.t6 t2.t60.t24.t33.t7.t13))
% 0.85/1.04 (step t2.t60.t24.t33.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t33.t7.t14 t2.t60.t24.t33.t7.t15))
% 0.85/1.04 (step t2.t60.t24.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t33.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t33.t6 t2.t60.t24.t33.t7))
% 0.85/1.04 (step t2.t60.t24.t33.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t33.t10.t5 t2.t60.t24.t33.t10.t6))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t33.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t33.t10.t9.t3 t2.t60.t24.t33.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t33.t10.t8 t2.t60.t24.t33.t10.t9))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t33.t10.t7 t2.t60.t24.t33.t10.t10))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t33.t10.t11 t2.t60.t24.t33.t10.t12))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t33.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t33.t10.t15.t2 t2.t60.t24.t33.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t33.t10.t14 t2.t60.t24.t33.t10.t15))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t33.t10.t13 t2.t60.t24.t33.t10.t16))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t33.t10.t4 t2.t60.t24.t33.t10.t17))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t33.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t33.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t33.t10.t19 t2.t60.t24.t33.t10.t20))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t33.t10.t18 t2.t60.t24.t33.t10.t21))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t33.t10.t22 t2.t60.t24.t33.t10.t23))
% 0.85/1.04 (step t2.t60.t24.t33.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t33.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t33.t10.t24 t2.t60.t24.t33.t10.t25))
% 0.85/1.04 (step t2.t60.t24.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t33.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t33.t9 t2.t60.t24.t33.t10))
% 0.85/1.04 (step t2.t60.t24.t33.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t33.t8 t2.t60.t24.t33.t11))
% 0.85/1.04 (step t2.t60.t24.t33.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t33.t5 t2.t60.t24.t33.t12 a4))
% 0.85/1.04 (step t2.t60.t24.t33.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t33.t4 t2.t60.t24.t33.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t24.t33.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t33.t14))
% 0.85/1.04 (step t2.t60.t24.t33.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t33.t14))
% 0.85/1.04 (step t2.t60.t24.t33.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t33.t16 t2.t60.t24.t33.t17))
% 0.85/1.04 (step t2.t60.t24.t33.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t33.t15 t2.t60.t24.t33.t18))
% 0.85/1.04 (step t2.t60.t24.t33.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t24.t33.t19 t2.t60.t24.t33.t20))
% 0.85/1.04 (step t2.t60.t24.t33.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t33.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t33.t21 t2.t60.t24.t33.t22))
% 0.85/1.04 (step t2.t60.t24.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t34 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t32 t2.t60.t24.t33))
% 0.85/1.04 (step t2.t60.t24.t35 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t36.t4 t2.t60.t24.t36.t5))
% 0.85/1.04 (step t2.t60.t24.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t36.t8.t3 t2.t60.t24.t36.t8.t4))
% 0.85/1.04 (step t2.t60.t24.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t36.t7 t2.t60.t24.t36.t8))
% 0.85/1.04 (step t2.t60.t24.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t36.t6 t2.t60.t24.t36.t9))
% 0.85/1.04 (step t2.t60.t24.t36.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t24.t36.t10 t2.t60.t24.t36.t11))
% 0.85/1.04 (step t2.t60.t24.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t36.t12 t2.t60.t24.t36.t13))
% 0.85/1.04 (step t2.t60.t24.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t36.t14 t2.t60.t24.t36.t15))
% 0.85/1.04 (step t2.t60.t24.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t24.t36.t16 t2.t60.t24.t36.t17))
% 0.85/1.04 (step t2.t60.t24.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t37 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t35 t2.t60.t24.t36))
% 0.85/1.04 (step t2.t60.t24.t38 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t34 t2.t60.t24.t37))
% 0.85/1.04 (step t2.t60.t24.t39 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t24.t31 t2.t60.t24.t38 a5))
% 0.85/1.04 (step t2.t60.t24.t40 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t24.t41 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t24.t42.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t42.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t24.t42.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t42.t5))
% 0.85/1.04 (step t2.t60.t24.t42.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t24.t42.t5))
% 0.85/1.04 (step t2.t60.t24.t42.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t24.t42.t6 t2.t60.t24.t42.t8))
% 0.85/1.04 (step t2.t60.t24.t42.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t24.t42.t7 t2.t60.t24.t42.t9))
% 0.85/1.04 (step t2.t60.t24.t42.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t24.t42.t6 t2.t60.t24.t42.t11))
% 0.85/1.04 (step t2.t60.t24.t42.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t24.t42.t10 t2.t60.t24.t42.t12))
% 0.85/1.04 (step t2.t60.t24.t42.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t24.t42.t6 t2.t60.t24.t42.t13))
% 0.85/1.04 (step t2.t60.t24.t42.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t42.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t42.t14 t2.t60.t24.t42.t15))
% 0.85/1.04 (step t2.t60.t24.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t43 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t41 t2.t60.t24.t42))
% 0.85/1.04 (step t2.t60.t24.t44 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t24.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t24.t45.t5 t2.t60.t24.t45.t6))
% 0.85/1.04 (step t2.t60.t24.t45.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t45.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t45.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t24.t45.t9.t3 t2.t60.t24.t45.t9.t4))
% 0.85/1.04 (step t2.t60.t24.t45.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t45.t8 t2.t60.t24.t45.t9))
% 0.85/1.04 (step t2.t60.t24.t45.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t24.t45.t7 t2.t60.t24.t45.t10))
% 0.85/1.04 (step t2.t60.t24.t45.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t45.t11 t2.t60.t24.t45.t12))
% 0.85/1.04 (step t2.t60.t24.t45.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t45.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t45.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t24.t45.t15.t2 t2.t60.t24.t45.t15.t3))
% 0.85/1.04 (step t2.t60.t24.t45.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t45.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t45.t14 t2.t60.t24.t45.t15))
% 0.85/1.04 (step t2.t60.t24.t45.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t24.t45.t13 t2.t60.t24.t45.t16))
% 0.85/1.04 (step t2.t60.t24.t45.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t24.t45.t4 t2.t60.t24.t45.t17))
% 0.85/1.04 (step t2.t60.t24.t45.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t24.t45.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t24.t45.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t24.t45.t20.t2))
% 0.85/1.04 (step t2.t60.t24.t45.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t45.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t45.t19 t2.t60.t24.t45.t20))
% 0.85/1.04 (step t2.t60.t24.t45.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t24.t45.t18 t2.t60.t24.t45.t21))
% 0.85/1.04 (step t2.t60.t24.t45.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t45.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t45.t22 t2.t60.t24.t45.t23))
% 0.85/1.04 (step t2.t60.t24.t45.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t24.t45.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t24.t45.t24 t2.t60.t24.t45.t25))
% 0.85/1.04 (step t2.t60.t24.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t46 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t24.t44 t2.t60.t24.t45))
% 0.85/1.04 (step t2.t60.t24.t47 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t24.t43 t2.t60.t24.t46))
% 0.85/1.04 (step t2.t60.t24.t48 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t24.t40 t2.t60.t24.t47 a4))
% 0.85/1.04 (step t2.t60.t24.t49 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t24.t3 a10 a9 t2.t60.t24.t12 t2.t60.t24.t21 t2.t60.t24.t30 t2.t60.t24.t39 t2.t60.t24.t48 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t24.t50 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t24.t49))
% 0.85/1.04 (step t2.t60.t24.t51 (cl (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule and :premises (t2.t60.t24.t49))
% 0.85/1.04 (anchor :step t2.t60.t24.t52 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t24.t52.t1 (cl (= X X)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t52.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t52.t3 (cl (= (@ Phi X) (@ Phi X))) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t52.t4 (cl (= (@ tptp.mnot (@ Phi X)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)))) :rule cong :premises (t2.t60.t24.t50 t2.t60.t24.t52.t3))
% 0.85/1.04 (step t2.t60.t24.t52.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t52.t6 (cl (= (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t52.t4 t2.t60.t24.t52.t5))
% 0.85/1.04 (step t2.t60.t24.t52 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t24.t53 (cl (= (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))))) :rule cong :premises (t2.t60.t24.t51 t2.t60.t24.t52))
% 0.85/1.04 (step t2.t60.t24.t54 (cl (= (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))))) :rule cong :premises (t2.t60.t24.t50 t2.t60.t24.t53))
% 0.85/1.04 (step t2.t60.t24.t55 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t24.t56 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t60.t24.t54 t2.t60.t24.t55))
% 0.85/1.04 (step t2.t60.t24 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t25 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t60.t23 t2.t60.t24))
% 0.85/1.04 (step t2.t60.t26 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t27 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t4 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t27.t5 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t27.t5.t1 (cl (= X X)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0))) :rule cong :premises (t2.t60.t27.t5.t3 t2.t60.t27.t5.t4))
% 0.85/1.04 (step t2.t60.t27.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule trans :premises (t2.t60.t27.t5.t5 t2.t60.t27.t5.t6))
% 0.85/1.04 (step t2.t60.t27.t5 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t27.t6 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule cong :premises (t2.t60.t27.t4 t2.t60.t27.t5))
% 0.85/1.04 (step t2.t60.t27.t7 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t27.t8 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t27.t8.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t27.t8.t2 :args ((X tptp.mu) (:= X X)))
% 0.85/1.04 (step t2.t60.t27.t8.t2.t1 (cl (= X X)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t8.t2.t2 (cl (= (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t8.t2.t4 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W))) :rule cong :premises (t2.t60.t27.t8.t2.t2 t2.t60.t27.t8.t2.t3))
% 0.85/1.04 (step t2.t60.t27.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W) (not (@ (@ Phi X) W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t8.t2.t6 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (not (@ (@ Phi X) W)))) :rule trans :premises (t2.t60.t27.t8.t2.t4 t2.t60.t27.t8.t2.t5))
% 0.85/1.04 (step t2.t60.t27.t8.t2 (cl (= (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t27.t8 (cl (= (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t27.t9 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t60.t27.t7 t2.t60.t27.t8))
% 0.85/1.04 (step t2.t60.t27.t10 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t60.t27.t6 t2.t60.t27.t9))
% 0.85/1.04 (step t2.t60.t27.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule cong :premises (t2.t60.t27.t3 t2.t60.t27.t10))
% 0.85/1.04 (step t2.t60.t27.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t27.t13 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t27.t13.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule cong :premises (t2.t60.t27.t13.t2))
% 0.85/1.04 (step t2.t60.t27.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t27.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t60.t27.t12 t2.t60.t27.t13))
% 0.85/1.04 (step t2.t60.t27.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t60.t27.t11 t2.t60.t27.t14))
% 0.85/1.04 (step t2.t60.t27.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t27.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t27.t15 t2.t60.t27.t16))
% 0.85/1.04 (step t2.t60.t27.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t27.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule trans :premises (t2.t60.t27.t17 t2.t60.t27.t18))
% 0.85/1.04 (step t2.t60.t27 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t28 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule cong :premises (t2.t60.t26 t2.t60.t27))
% 0.85/1.04 (step t2.t60.t29 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule trans :premises (t2.t60.t25 t2.t60.t28))
% 0.85/1.04 (step t2.t60.t30 (cl (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule resolution :premises (t2.t60.t22 t2.t60.t29 a11))
% 0.85/1.04 (step t2.t60.t31 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t32 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t7.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t7.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t6 t2.t60.t33.t7.t7.t7.t7.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t7 t2.t60.t33.t7.t7.t7.t7.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t6 t2.t60.t33.t7.t7.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t10 t2.t60.t33.t7.t7.t7.t7.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t6 t2.t60.t33.t7.t7.t7.t7.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t7.t14 t2.t60.t33.t7.t7.t7.t7.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t6 t2.t60.t33.t7.t7.t7.t7))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t5 t2.t60.t33.t7.t7.t7.t10.t6))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t9.t3 t2.t60.t33.t7.t7.t7.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t8 t2.t60.t33.t7.t7.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t7 t2.t60.t33.t7.t7.t7.t10.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t11 t2.t60.t33.t7.t7.t7.t10.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t15.t2 t2.t60.t33.t7.t7.t7.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t14 t2.t60.t33.t7.t7.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t13 t2.t60.t33.t7.t7.t7.t10.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t4 t2.t60.t33.t7.t7.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t19 t2.t60.t33.t7.t7.t7.t10.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t18 t2.t60.t33.t7.t7.t7.t10.t21))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t10.t22 t2.t60.t33.t7.t7.t7.t10.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t10.t24 t2.t60.t33.t7.t7.t7.t10.t25))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t9 t2.t60.t33.t7.t7.t7.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t7.t7.t7.t8 t2.t60.t33.t7.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t7.t7.t7.t5 t2.t60.t33.t7.t7.t7.t12 a4))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t7.t7.t4 t2.t60.t33.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t7.t7.t14))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t7.t7.t14))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t16 t2.t60.t33.t7.t7.t7.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t15 t2.t60.t33.t7.t7.t7.t18))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t19 t2.t60.t33.t7.t7.t7.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t7.t21 t2.t60.t33.t7.t7.t7.t22))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t7.t6 t2.t60.t33.t7.t7.t7))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t10.t4 t2.t60.t33.t7.t7.t10.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t7.t10.t8.t3 t2.t60.t33.t7.t7.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t10.t7 t2.t60.t33.t7.t7.t10.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t10.t6 t2.t60.t33.t7.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t7.t10.t10 t2.t60.t33.t7.t7.t10.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t10.t12 t2.t60.t33.t7.t7.t10.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t10.t14 t2.t60.t33.t7.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t7.t7.t10.t16 t2.t60.t33.t7.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t7.t7.t9 t2.t60.t33.t7.t7.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t7.t8 t2.t60.t33.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t7.t7.t5 t2.t60.t33.t7.t7.t12 a5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t7.t16.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t7.t16.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t6 t2.t60.t33.t7.t7.t16.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t7 t2.t60.t33.t7.t7.t16.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t6 t2.t60.t33.t7.t7.t16.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t10 t2.t60.t33.t7.t7.t16.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t6 t2.t60.t33.t7.t7.t16.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t16.t14 t2.t60.t33.t7.t7.t16.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t7.t15 t2.t60.t33.t7.t7.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t5 t2.t60.t33.t7.t7.t19.t6))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t9.t3 t2.t60.t33.t7.t7.t19.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t8 t2.t60.t33.t7.t7.t19.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t7 t2.t60.t33.t7.t7.t19.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t11 t2.t60.t33.t7.t7.t19.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t15.t2 t2.t60.t33.t7.t7.t19.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t14 t2.t60.t33.t7.t7.t19.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t13 t2.t60.t33.t7.t7.t19.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t4 t2.t60.t33.t7.t7.t19.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t19 t2.t60.t33.t7.t7.t19.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t18 t2.t60.t33.t7.t7.t19.t21))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t19.t22 t2.t60.t33.t7.t7.t19.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t7.t19.t24 t2.t60.t33.t7.t7.t19.t25))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t7.t7.t18 t2.t60.t33.t7.t7.t19))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t7.t7.t17 t2.t60.t33.t7.t7.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t7.t7.t14 t2.t60.t33.t7.t7.t21 a4))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t7.t4 t2.t60.t33.t7.t7.t13 t2.t60.t33.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t7.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t7.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t7.t25 t2.t60.t33.t7.t7.t26))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t7.t7.t24 t2.t60.t33.t7.t7.t27))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t33.t7.t7.t28 t2.t60.t33.t7.t7.t29))
% 0.85/1.04 (step t2.t60.t33.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t7.t30 t2.t60.t33.t7.t7.t31))
% 0.85/1.04 (step t2.t60.t33.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t6 t2.t60.t33.t7.t7))
% 0.85/1.04 (step t2.t60.t33.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t10.t4 t2.t60.t33.t7.t10.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t10.t8.t3 t2.t60.t33.t7.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t10.t7 t2.t60.t33.t7.t10.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t10.t6 t2.t60.t33.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t10.t10 t2.t60.t33.t7.t10.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t33.t7.t10.t12 t2.t60.t33.t7.t10.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t10.t14 t2.t60.t33.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t7.t10.t16 t2.t60.t33.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t7.t9 t2.t60.t33.t7.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t8 t2.t60.t33.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t7.t5 t2.t60.t33.t7.t12 a6))
% 0.85/1.04 (step t2.t60.t33.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t16.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t16.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t6 t2.t60.t33.t7.t16.t7.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t7 t2.t60.t33.t7.t16.t7.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t6 t2.t60.t33.t7.t16.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t10 t2.t60.t33.t7.t16.t7.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t6 t2.t60.t33.t7.t16.t7.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t16.t7.t14 t2.t60.t33.t7.t16.t7.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t16.t6 t2.t60.t33.t7.t16.t7))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t5 t2.t60.t33.t7.t16.t10.t6))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t9.t3 t2.t60.t33.t7.t16.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t8 t2.t60.t33.t7.t16.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t7 t2.t60.t33.t7.t16.t10.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t11 t2.t60.t33.t7.t16.t10.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t15.t2 t2.t60.t33.t7.t16.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t14 t2.t60.t33.t7.t16.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t13 t2.t60.t33.t7.t16.t10.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t4 t2.t60.t33.t7.t16.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t19 t2.t60.t33.t7.t16.t10.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t18 t2.t60.t33.t7.t16.t10.t21))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t16.t10.t22 t2.t60.t33.t7.t16.t10.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t16.t10.t24 t2.t60.t33.t7.t16.t10.t25))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t7.t16.t9 t2.t60.t33.t7.t16.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t7.t16.t8 t2.t60.t33.t7.t16.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t7.t16.t5 t2.t60.t33.t7.t16.t12 a4))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t16.t4 t2.t60.t33.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t16.t14))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t16.t14))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t16.t16 t2.t60.t33.t7.t16.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t16.t15 t2.t60.t33.t7.t16.t18))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t33.t7.t16.t19 t2.t60.t33.t7.t16.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t16.t21 t2.t60.t33.t7.t16.t22))
% 0.85/1.04 (step t2.t60.t33.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t15 t2.t60.t33.t7.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t19.t4 t2.t60.t33.t7.t19.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t19.t8.t3 t2.t60.t33.t7.t19.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t19.t7 t2.t60.t33.t7.t19.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t19.t6 t2.t60.t33.t7.t19.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t19.t10 t2.t60.t33.t7.t19.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t19.t12 t2.t60.t33.t7.t19.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t19.t14 t2.t60.t33.t7.t19.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t7.t19.t16 t2.t60.t33.t7.t19.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t7.t18 t2.t60.t33.t7.t19))
% 0.85/1.04 (step t2.t60.t33.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t17 t2.t60.t33.t7.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t7.t14 t2.t60.t33.t7.t21 a5))
% 0.85/1.04 (step t2.t60.t33.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t7.t25.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t7.t25.t5))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t7.t25.t6 t2.t60.t33.t7.t25.t8))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t7.t25.t7 t2.t60.t33.t7.t25.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t7.t25.t6 t2.t60.t33.t7.t25.t11))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t7.t25.t10 t2.t60.t33.t7.t25.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t7.t25.t6 t2.t60.t33.t7.t25.t13))
% 0.85/1.04 (step t2.t60.t33.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t25.t14 t2.t60.t33.t7.t25.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t7.t24 t2.t60.t33.t7.t25))
% 0.85/1.04 (step t2.t60.t33.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t7.t28.t5 t2.t60.t33.t7.t28.t6))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t7.t28.t9.t3 t2.t60.t33.t7.t28.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t28.t8 t2.t60.t33.t7.t28.t9))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t7.t28.t7 t2.t60.t33.t7.t28.t10))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t28.t11 t2.t60.t33.t7.t28.t12))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t7.t28.t15.t2 t2.t60.t33.t7.t28.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t28.t14 t2.t60.t33.t7.t28.t15))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t7.t28.t13 t2.t60.t33.t7.t28.t16))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t7.t28.t4 t2.t60.t33.t7.t28.t17))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t7.t28.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t28.t19 t2.t60.t33.t7.t28.t20))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t7.t28.t18 t2.t60.t33.t7.t28.t21))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t28.t22 t2.t60.t33.t7.t28.t23))
% 0.85/1.04 (step t2.t60.t33.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t7.t28.t24 t2.t60.t33.t7.t28.t25))
% 0.85/1.04 (step t2.t60.t33.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t7.t27 t2.t60.t33.t7.t28))
% 0.85/1.04 (step t2.t60.t33.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t7.t26 t2.t60.t33.t7.t29))
% 0.85/1.04 (step t2.t60.t33.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t7.t23 t2.t60.t33.t7.t30 a4))
% 0.85/1.04 (step t2.t60.t33.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t7.t4 t2.t60.t33.t7.t13 t2.t60.t33.t7.t22 t2.t60.t33.t7.t31 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t33.t7.t32))
% 0.85/1.04 (step t2.t60.t33.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t33.t7.t32))
% 0.85/1.04 (step t2.t60.t33.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t33.t7.t34 t2.t60.t33.t7.t35))
% 0.85/1.04 (step t2.t60.t33.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t33.t7.t36 t2.t60.t33.t7.t37))
% 0.85/1.04 (step t2.t60.t33.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t33.t7.t33 t2.t60.t33.t7.t38))
% 0.85/1.04 (step t2.t60.t33.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t33.t7.t34 t2.t60.t33.t7.t37))
% 0.85/1.04 (step t2.t60.t33.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t33.t7.t40 t2.t60.t33.t7.t35))
% 0.85/1.04 (step t2.t60.t33.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t33.t7.t39 t2.t60.t33.t7.t41))
% 0.85/1.04 (step t2.t60.t33.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t7.t42 t2.t60.t33.t7.t43))
% 0.85/1.04 (step t2.t60.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t6 t2.t60.t33.t7))
% 0.85/1.04 (step t2.t60.t33.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t33.t10.t5 t2.t60.t33.t10.t6))
% 0.85/1.04 (step t2.t60.t33.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t33.t10.t7 t2.t60.t33.t10.t8))
% 0.85/1.04 (step t2.t60.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t10.t4 t2.t60.t33.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t10.t12.t3))
% 0.85/1.04 (step t2.t60.t33.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t10.t12.t4 t2.t60.t33.t10.t12.t5))
% 0.85/1.04 (step t2.t60.t33.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t10.t12.t6))
% 0.85/1.04 (step t2.t60.t33.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t33.t10.t11 t2.t60.t33.t10.t12))
% 0.85/1.04 (step t2.t60.t33.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t33.t10.t10 t2.t60.t33.t10.t13))
% 0.85/1.04 (step t2.t60.t33.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t33.t10.t15 t2.t60.t33.t10.t16))
% 0.85/1.04 (step t2.t60.t33.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t33.t10.t17 t2.t60.t33.t10.t18))
% 0.85/1.04 (step t2.t60.t33.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t10.t14 t2.t60.t33.t10.t19))
% 0.85/1.04 (step t2.t60.t33.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t10.t22.t3))
% 0.85/1.04 (step t2.t60.t33.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t10.t22.t2 t2.t60.t33.t10.t22.t4))
% 0.85/1.04 (step t2.t60.t33.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t33.t10.t22.t5))
% 0.85/1.04 (step t2.t60.t33.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t10.t21 t2.t60.t33.t10.t22))
% 0.85/1.04 (step t2.t60.t33.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t10.t20 t2.t60.t33.t10.t23))
% 0.85/1.04 (step t2.t60.t33.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t10.t24 t2.t60.t33.t10.t25))
% 0.85/1.04 (step t2.t60.t33.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t33.t10.t26 t2.t60.t33.t10.t27))
% 0.85/1.04 (step t2.t60.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t33.t9 t2.t60.t33.t10))
% 0.85/1.04 (step t2.t60.t33.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t33.t8 t2.t60.t33.t11))
% 0.85/1.04 (step t2.t60.t33.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t33.t5 t2.t60.t33.t12 a7))
% 0.85/1.04 (step t2.t60.t33.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t16.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t16.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t6 t2.t60.t33.t16.t7.t7.t8))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t7 t2.t60.t33.t16.t7.t7.t9))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t6 t2.t60.t33.t16.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t10 t2.t60.t33.t16.t7.t7.t12))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t6 t2.t60.t33.t16.t7.t7.t13))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t7.t7.t14 t2.t60.t33.t16.t7.t7.t15))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t16.t7.t6 t2.t60.t33.t16.t7.t7))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t5 t2.t60.t33.t16.t7.t10.t6))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t9.t3 t2.t60.t33.t16.t7.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t8 t2.t60.t33.t16.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t7 t2.t60.t33.t16.t7.t10.t10))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t11 t2.t60.t33.t16.t7.t10.t12))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t15.t2 t2.t60.t33.t16.t7.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t14 t2.t60.t33.t16.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t13 t2.t60.t33.t16.t7.t10.t16))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t4 t2.t60.t33.t16.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t19 t2.t60.t33.t16.t7.t10.t20))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t18 t2.t60.t33.t16.t7.t10.t21))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t7.t10.t22 t2.t60.t33.t16.t7.t10.t23))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t16.t7.t10.t24 t2.t60.t33.t16.t7.t10.t25))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t16.t7.t9 t2.t60.t33.t16.t7.t10))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t16.t7.t8 t2.t60.t33.t16.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t16.t7.t5 t2.t60.t33.t16.t7.t12 a4))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t16.t7.t4 t2.t60.t33.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t16.t7.t14))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t16.t7.t14))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t16.t7.t16 t2.t60.t33.t16.t7.t17))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t16.t7.t15 t2.t60.t33.t16.t7.t18))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t33.t16.t7.t19 t2.t60.t33.t16.t7.t20))
% 0.85/1.04 (step t2.t60.t33.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t7.t21 t2.t60.t33.t16.t7.t22))
% 0.85/1.04 (step t2.t60.t33.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t16.t6 t2.t60.t33.t16.t7))
% 0.85/1.04 (step t2.t60.t33.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t16.t10.t4 t2.t60.t33.t16.t10.t5))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t16.t10.t8.t3 t2.t60.t33.t16.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t10.t7 t2.t60.t33.t16.t10.t8))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t10.t6 t2.t60.t33.t16.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t33.t16.t10.t10 t2.t60.t33.t16.t10.t11))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t10.t12 t2.t60.t33.t16.t10.t13))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t10.t14 t2.t60.t33.t16.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t16.t10.t16 t2.t60.t33.t16.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t16.t9 t2.t60.t33.t16.t10))
% 0.85/1.04 (step t2.t60.t33.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t16.t8 t2.t60.t33.t16.t11))
% 0.85/1.04 (step t2.t60.t33.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t16.t5 t2.t60.t33.t16.t12 a5))
% 0.85/1.04 (step t2.t60.t33.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t16.t16.t5))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t16.t16.t5))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t16.t16.t6 t2.t60.t33.t16.t16.t8))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t16.t16.t7 t2.t60.t33.t16.t16.t9))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t16.t16.t6 t2.t60.t33.t16.t16.t11))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t16.t16.t10 t2.t60.t33.t16.t16.t12))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t16.t16.t6 t2.t60.t33.t16.t16.t13))
% 0.85/1.04 (step t2.t60.t33.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t16.t14 t2.t60.t33.t16.t16.t15))
% 0.85/1.04 (step t2.t60.t33.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t16.t15 t2.t60.t33.t16.t16))
% 0.85/1.04 (step t2.t60.t33.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t16.t19.t5 t2.t60.t33.t16.t19.t6))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t16.t19.t9.t3 t2.t60.t33.t16.t19.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t19.t8 t2.t60.t33.t16.t19.t9))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t16.t19.t7 t2.t60.t33.t16.t19.t10))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t16.t19.t11 t2.t60.t33.t16.t19.t12))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t16.t19.t15.t2 t2.t60.t33.t16.t19.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t16.t19.t14 t2.t60.t33.t16.t19.t15))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t16.t19.t13 t2.t60.t33.t16.t19.t16))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t16.t19.t4 t2.t60.t33.t16.t19.t17))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t16.t19.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t16.t19.t19 t2.t60.t33.t16.t19.t20))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t16.t19.t18 t2.t60.t33.t16.t19.t21))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t19.t22 t2.t60.t33.t16.t19.t23))
% 0.85/1.04 (step t2.t60.t33.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t16.t19.t24 t2.t60.t33.t16.t19.t25))
% 0.85/1.04 (step t2.t60.t33.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t16.t18 t2.t60.t33.t16.t19))
% 0.85/1.04 (step t2.t60.t33.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t16.t17 t2.t60.t33.t16.t20))
% 0.85/1.04 (step t2.t60.t33.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t16.t14 t2.t60.t33.t16.t21 a4))
% 0.85/1.04 (step t2.t60.t33.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t16.t4 t2.t60.t33.t16.t13 t2.t60.t33.t16.t22 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t16.t23))
% 0.85/1.04 (step t2.t60.t33.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t16.t23))
% 0.85/1.04 (step t2.t60.t33.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t16.t25 t2.t60.t33.t16.t26))
% 0.85/1.04 (step t2.t60.t33.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t16.t24 t2.t60.t33.t16.t27))
% 0.85/1.04 (step t2.t60.t33.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t33.t16.t28 t2.t60.t33.t16.t29))
% 0.85/1.04 (step t2.t60.t33.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t16.t30 t2.t60.t33.t16.t31))
% 0.85/1.04 (step t2.t60.t33.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t15 t2.t60.t33.t16))
% 0.85/1.04 (step t2.t60.t33.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t19.t4 t2.t60.t33.t19.t5))
% 0.85/1.04 (step t2.t60.t33.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t19.t8.t3 t2.t60.t33.t19.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t19.t7 t2.t60.t33.t19.t8))
% 0.85/1.04 (step t2.t60.t33.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t19.t6 t2.t60.t33.t19.t9))
% 0.85/1.04 (step t2.t60.t33.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t33.t19.t10 t2.t60.t33.t19.t11))
% 0.85/1.04 (step t2.t60.t33.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t33.t19.t12 t2.t60.t33.t19.t13))
% 0.85/1.04 (step t2.t60.t33.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t19.t14 t2.t60.t33.t19.t15))
% 0.85/1.04 (step t2.t60.t33.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t19.t16 t2.t60.t33.t19.t17))
% 0.85/1.04 (step t2.t60.t33.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t18 t2.t60.t33.t19))
% 0.85/1.04 (step t2.t60.t33.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t17 t2.t60.t33.t20))
% 0.85/1.04 (step t2.t60.t33.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t14 t2.t60.t33.t21 a6))
% 0.85/1.04 (step t2.t60.t33.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t25.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t25.t7.t5))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t25.t7.t6 t2.t60.t33.t25.t7.t8))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t25.t7.t7 t2.t60.t33.t25.t7.t9))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t25.t7.t6 t2.t60.t33.t25.t7.t11))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t25.t7.t10 t2.t60.t33.t25.t7.t12))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t25.t7.t6 t2.t60.t33.t25.t7.t13))
% 0.85/1.04 (step t2.t60.t33.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t25.t7.t14 t2.t60.t33.t25.t7.t15))
% 0.85/1.04 (step t2.t60.t33.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t25.t6 t2.t60.t33.t25.t7))
% 0.85/1.04 (step t2.t60.t33.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t25.t10.t5 t2.t60.t33.t25.t10.t6))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t25.t10.t9.t3 t2.t60.t33.t25.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t25.t10.t8 t2.t60.t33.t25.t10.t9))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t25.t10.t7 t2.t60.t33.t25.t10.t10))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t25.t10.t11 t2.t60.t33.t25.t10.t12))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t25.t10.t15.t2 t2.t60.t33.t25.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t25.t10.t14 t2.t60.t33.t25.t10.t15))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t25.t10.t13 t2.t60.t33.t25.t10.t16))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t25.t10.t4 t2.t60.t33.t25.t10.t17))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t25.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t25.t10.t19 t2.t60.t33.t25.t10.t20))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t25.t10.t18 t2.t60.t33.t25.t10.t21))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t25.t10.t22 t2.t60.t33.t25.t10.t23))
% 0.85/1.04 (step t2.t60.t33.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t25.t10.t24 t2.t60.t33.t25.t10.t25))
% 0.85/1.04 (step t2.t60.t33.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t25.t9 t2.t60.t33.t25.t10))
% 0.85/1.04 (step t2.t60.t33.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t25.t8 t2.t60.t33.t25.t11))
% 0.85/1.04 (step t2.t60.t33.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t25.t5 t2.t60.t33.t25.t12 a4))
% 0.85/1.04 (step t2.t60.t33.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t25.t4 t2.t60.t33.t25.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t25.t14))
% 0.85/1.04 (step t2.t60.t33.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t25.t14))
% 0.85/1.04 (step t2.t60.t33.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t25.t16 t2.t60.t33.t25.t17))
% 0.85/1.04 (step t2.t60.t33.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t25.t15 t2.t60.t33.t25.t18))
% 0.85/1.04 (step t2.t60.t33.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t33.t25.t19 t2.t60.t33.t25.t20))
% 0.85/1.04 (step t2.t60.t33.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t25.t21 t2.t60.t33.t25.t22))
% 0.85/1.04 (step t2.t60.t33.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t24 t2.t60.t33.t25))
% 0.85/1.04 (step t2.t60.t33.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t28.t4 t2.t60.t33.t28.t5))
% 0.85/1.04 (step t2.t60.t33.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t28.t8.t3 t2.t60.t33.t28.t8.t4))
% 0.85/1.04 (step t2.t60.t33.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t28.t7 t2.t60.t33.t28.t8))
% 0.85/1.04 (step t2.t60.t33.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t28.t6 t2.t60.t33.t28.t9))
% 0.85/1.04 (step t2.t60.t33.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t33.t28.t10 t2.t60.t33.t28.t11))
% 0.85/1.04 (step t2.t60.t33.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t28.t12 t2.t60.t33.t28.t13))
% 0.85/1.04 (step t2.t60.t33.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t28.t14 t2.t60.t33.t28.t15))
% 0.85/1.04 (step t2.t60.t33.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t33.t28.t16 t2.t60.t33.t28.t17))
% 0.85/1.04 (step t2.t60.t33.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t33.t27 t2.t60.t33.t28))
% 0.85/1.04 (step t2.t60.t33.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t26 t2.t60.t33.t29))
% 0.85/1.04 (step t2.t60.t33.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t33.t23 t2.t60.t33.t30 a5))
% 0.85/1.04 (step t2.t60.t33.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t33.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t33.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t34.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t34.t5))
% 0.85/1.04 (step t2.t60.t33.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t33.t34.t5))
% 0.85/1.04 (step t2.t60.t33.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t33.t34.t6 t2.t60.t33.t34.t8))
% 0.85/1.04 (step t2.t60.t33.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t33.t34.t7 t2.t60.t33.t34.t9))
% 0.85/1.04 (step t2.t60.t33.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t33.t34.t6 t2.t60.t33.t34.t11))
% 0.85/1.04 (step t2.t60.t33.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t33.t34.t10 t2.t60.t33.t34.t12))
% 0.85/1.04 (step t2.t60.t33.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t33.t34.t6 t2.t60.t33.t34.t13))
% 0.85/1.04 (step t2.t60.t33.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t34.t14 t2.t60.t33.t34.t15))
% 0.85/1.04 (step t2.t60.t33.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t33.t33 t2.t60.t33.t34))
% 0.85/1.04 (step t2.t60.t33.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t33.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t33.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t33.t37.t5 t2.t60.t33.t37.t6))
% 0.85/1.04 (step t2.t60.t33.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t33.t37.t9.t3 t2.t60.t33.t37.t9.t4))
% 0.85/1.04 (step t2.t60.t33.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t37.t8 t2.t60.t33.t37.t9))
% 0.85/1.04 (step t2.t60.t33.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t33.t37.t7 t2.t60.t33.t37.t10))
% 0.85/1.04 (step t2.t60.t33.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t37.t11 t2.t60.t33.t37.t12))
% 0.85/1.04 (step t2.t60.t33.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t33.t37.t15.t2 t2.t60.t33.t37.t15.t3))
% 0.85/1.04 (step t2.t60.t33.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t37.t14 t2.t60.t33.t37.t15))
% 0.85/1.04 (step t2.t60.t33.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t33.t37.t13 t2.t60.t33.t37.t16))
% 0.85/1.04 (step t2.t60.t33.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t33.t37.t4 t2.t60.t33.t37.t17))
% 0.85/1.04 (step t2.t60.t33.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t33.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t33.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t33.t37.t20.t2))
% 0.85/1.04 (step t2.t60.t33.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t37.t19 t2.t60.t33.t37.t20))
% 0.85/1.04 (step t2.t60.t33.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t33.t37.t18 t2.t60.t33.t37.t21))
% 0.85/1.04 (step t2.t60.t33.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t37.t22 t2.t60.t33.t37.t23))
% 0.85/1.04 (step t2.t60.t33.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t33.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t33.t37.t24 t2.t60.t33.t37.t25))
% 0.85/1.04 (step t2.t60.t33.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t33.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t33.t36 t2.t60.t33.t37))
% 0.85/1.04 (step t2.t60.t33.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t33.t35 t2.t60.t33.t38))
% 0.85/1.04 (step t2.t60.t33.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t33.t32 t2.t60.t33.t39 a4))
% 0.85/1.04 (step t2.t60.t33.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t33.t4 t2.t60.t33.t13 t2.t60.t33.t22 t2.t60.t33.t31 t2.t60.t33.t40 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t33.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t33.t41))
% 0.85/1.04 (step t2.t60.t33.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t60.t33.t41))
% 0.85/1.04 (step t2.t60.t33.t44 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t60.t33.t43 t2.t60.t33.t44))
% 0.85/1.04 (step t2.t60.t33.t46 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t60.t33.t45 t2.t60.t33.t46))
% 0.85/1.04 (step t2.t60.t33.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t60.t33.t42 t2.t60.t33.t47))
% 0.85/1.04 (step t2.t60.t33.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t33.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t60.t33.t48 t2.t60.t33.t49))
% 0.85/1.04 (step t2.t60.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t34 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t32 t2.t60.t33))
% 0.85/1.04 (step t2.t60.t35 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t36.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t60.t36.t5 t2.t60.t36.t6))
% 0.85/1.04 (step t2.t60.t36.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t36.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t36.t7 t2.t60.t36.t8))
% 0.85/1.04 (step t2.t60.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t36.t4 t2.t60.t36.t9))
% 0.85/1.04 (step t2.t60.t36.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t36.t12 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t36.t12.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t36.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t60.t36.t12.t2))
% 0.85/1.04 (step t2.t60.t36.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t36.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t60.t36.t12.t3 t2.t60.t36.t12.t4))
% 0.85/1.04 (step t2.t60.t36.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t36.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t36.t11 t2.t60.t36.t12))
% 0.85/1.04 (step t2.t60.t36.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t60.t36.t10 t2.t60.t36.t13))
% 0.85/1.04 (step t2.t60.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t36.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t36.t14 t2.t60.t36.t15))
% 0.85/1.04 (step t2.t60.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t36.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t36.t16 t2.t60.t36.t17))
% 0.85/1.04 (step t2.t60.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t37 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t35 t2.t60.t36))
% 0.85/1.04 (step t2.t60.t38 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t34 t2.t60.t37))
% 0.85/1.04 (step t2.t60.t39 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t31 t2.t60.t38 a8))
% 0.85/1.04 (step t2.t60.t40 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t41 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t7.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t7.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t6 t2.t60.t42.t7.t7.t7.t8))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t7 t2.t60.t42.t7.t7.t7.t9))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t6 t2.t60.t42.t7.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t10 t2.t60.t42.t7.t7.t7.t12))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t6 t2.t60.t42.t7.t7.t7.t13))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t7.t7.t14 t2.t60.t42.t7.t7.t7.t15))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t7.t7.t6 t2.t60.t42.t7.t7.t7))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t5 t2.t60.t42.t7.t7.t10.t6))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t9.t3 t2.t60.t42.t7.t7.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t8 t2.t60.t42.t7.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t7 t2.t60.t42.t7.t7.t10.t10))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t11 t2.t60.t42.t7.t7.t10.t12))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t15.t2 t2.t60.t42.t7.t7.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t14 t2.t60.t42.t7.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t13 t2.t60.t42.t7.t7.t10.t16))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t4 t2.t60.t42.t7.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t19 t2.t60.t42.t7.t7.t10.t20))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t18 t2.t60.t42.t7.t7.t10.t21))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t7.t10.t22 t2.t60.t42.t7.t7.t10.t23))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t7.t7.t10.t24 t2.t60.t42.t7.t7.t10.t25))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t42.t7.t7.t9 t2.t60.t42.t7.t7.t10))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t42.t7.t7.t8 t2.t60.t42.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t42.t7.t7.t5 t2.t60.t42.t7.t7.t12 a4))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t7.t7.t4 t2.t60.t42.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t7.t7.t14))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t7.t7.t14))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t7.t7.t16 t2.t60.t42.t7.t7.t17))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t7.t7.t15 t2.t60.t42.t7.t7.t18))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t42.t7.t7.t19 t2.t60.t42.t7.t7.t20))
% 0.85/1.04 (step t2.t60.t42.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t7.t21 t2.t60.t42.t7.t7.t22))
% 0.85/1.04 (step t2.t60.t42.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t7.t6 t2.t60.t42.t7.t7))
% 0.85/1.04 (step t2.t60.t42.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t7.t10.t4 t2.t60.t42.t7.t10.t5))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t7.t10.t8.t3 t2.t60.t42.t7.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t10.t7 t2.t60.t42.t7.t10.t8))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t10.t6 t2.t60.t42.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t42.t7.t10.t10 t2.t60.t42.t7.t10.t11))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t10.t12 t2.t60.t42.t7.t10.t13))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t10.t14 t2.t60.t42.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t42.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t42.t7.t10.t16 t2.t60.t42.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t42.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t42.t7.t9 t2.t60.t42.t7.t10))
% 0.85/1.04 (step t2.t60.t42.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t7.t8 t2.t60.t42.t7.t11))
% 0.85/1.04 (step t2.t60.t42.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t42.t7.t5 t2.t60.t42.t7.t12 a5))
% 0.85/1.04 (step t2.t60.t42.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t7.t16.t5))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t7.t16.t5))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t7.t16.t6 t2.t60.t42.t7.t16.t8))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t7.t16.t7 t2.t60.t42.t7.t16.t9))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t42.t7.t16.t6 t2.t60.t42.t7.t16.t11))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t42.t7.t16.t10 t2.t60.t42.t7.t16.t12))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t42.t7.t16.t6 t2.t60.t42.t7.t16.t13))
% 0.85/1.04 (step t2.t60.t42.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t16.t14 t2.t60.t42.t7.t16.t15))
% 0.85/1.04 (step t2.t60.t42.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t7.t15 t2.t60.t42.t7.t16))
% 0.85/1.04 (step t2.t60.t42.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t7.t19.t5 t2.t60.t42.t7.t19.t6))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t7.t19.t9.t3 t2.t60.t42.t7.t19.t9.t4))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t19.t8 t2.t60.t42.t7.t19.t9))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t7.t19.t7 t2.t60.t42.t7.t19.t10))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t7.t19.t11 t2.t60.t42.t7.t19.t12))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t42.t7.t19.t15.t2 t2.t60.t42.t7.t19.t15.t3))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t7.t19.t14 t2.t60.t42.t7.t19.t15))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t7.t19.t13 t2.t60.t42.t7.t19.t16))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t42.t7.t19.t4 t2.t60.t42.t7.t19.t17))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t7.t19.t20.t2))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t7.t19.t19 t2.t60.t42.t7.t19.t20))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t7.t19.t18 t2.t60.t42.t7.t19.t21))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t19.t22 t2.t60.t42.t7.t19.t23))
% 0.85/1.04 (step t2.t60.t42.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t7.t19.t24 t2.t60.t42.t7.t19.t25))
% 0.85/1.04 (step t2.t60.t42.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t42.t7.t18 t2.t60.t42.t7.t19))
% 0.85/1.04 (step t2.t60.t42.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t42.t7.t17 t2.t60.t42.t7.t20))
% 0.85/1.04 (step t2.t60.t42.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t42.t7.t14 t2.t60.t42.t7.t21 a4))
% 0.85/1.04 (step t2.t60.t42.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t7.t4 t2.t60.t42.t7.t13 t2.t60.t42.t7.t22 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t7.t23))
% 0.85/1.04 (step t2.t60.t42.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t7.t23))
% 0.85/1.04 (step t2.t60.t42.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t42.t7.t25 t2.t60.t42.t7.t26))
% 0.85/1.04 (step t2.t60.t42.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t42.t7.t24 t2.t60.t42.t7.t27))
% 0.85/1.04 (step t2.t60.t42.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t42.t7.t28 t2.t60.t42.t7.t29))
% 0.85/1.04 (step t2.t60.t42.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t7.t30 t2.t60.t42.t7.t31))
% 0.85/1.04 (step t2.t60.t42.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t6 t2.t60.t42.t7))
% 0.85/1.04 (step t2.t60.t42.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t10.t4 t2.t60.t42.t10.t5))
% 0.85/1.04 (step t2.t60.t42.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t10.t8.t3 t2.t60.t42.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t42.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t10.t7 t2.t60.t42.t10.t8))
% 0.85/1.04 (step t2.t60.t42.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t10.t6 t2.t60.t42.t10.t9))
% 0.85/1.04 (step t2.t60.t42.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t42.t10.t10 t2.t60.t42.t10.t11))
% 0.85/1.04 (step t2.t60.t42.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t42.t10.t12 t2.t60.t42.t10.t13))
% 0.85/1.04 (step t2.t60.t42.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t10.t14 t2.t60.t42.t10.t15))
% 0.85/1.04 (step t2.t60.t42.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t42.t10.t16 t2.t60.t42.t10.t17))
% 0.85/1.04 (step t2.t60.t42.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t42.t9 t2.t60.t42.t10))
% 0.85/1.04 (step t2.t60.t42.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t8 t2.t60.t42.t11))
% 0.85/1.04 (step t2.t60.t42.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t42.t5 t2.t60.t42.t12 a6))
% 0.85/1.04 (step t2.t60.t42.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t16.t7.t5))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t16.t7.t5))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t16.t7.t6 t2.t60.t42.t16.t7.t8))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t16.t7.t7 t2.t60.t42.t16.t7.t9))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t42.t16.t7.t6 t2.t60.t42.t16.t7.t11))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t42.t16.t7.t10 t2.t60.t42.t16.t7.t12))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t42.t16.t7.t6 t2.t60.t42.t16.t7.t13))
% 0.85/1.04 (step t2.t60.t42.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t16.t7.t14 t2.t60.t42.t16.t7.t15))
% 0.85/1.04 (step t2.t60.t42.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t16.t6 t2.t60.t42.t16.t7))
% 0.85/1.04 (step t2.t60.t42.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t16.t10.t5 t2.t60.t42.t16.t10.t6))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t16.t10.t9.t3 t2.t60.t42.t16.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t16.t10.t8 t2.t60.t42.t16.t10.t9))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t16.t10.t7 t2.t60.t42.t16.t10.t10))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t16.t10.t11 t2.t60.t42.t16.t10.t12))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t42.t16.t10.t15.t2 t2.t60.t42.t16.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t16.t10.t14 t2.t60.t42.t16.t10.t15))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t16.t10.t13 t2.t60.t42.t16.t10.t16))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t42.t16.t10.t4 t2.t60.t42.t16.t10.t17))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t16.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t16.t10.t19 t2.t60.t42.t16.t10.t20))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t16.t10.t18 t2.t60.t42.t16.t10.t21))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t16.t10.t22 t2.t60.t42.t16.t10.t23))
% 0.85/1.04 (step t2.t60.t42.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t16.t10.t24 t2.t60.t42.t16.t10.t25))
% 0.85/1.04 (step t2.t60.t42.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t42.t16.t9 t2.t60.t42.t16.t10))
% 0.85/1.04 (step t2.t60.t42.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t42.t16.t8 t2.t60.t42.t16.t11))
% 0.85/1.04 (step t2.t60.t42.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t42.t16.t5 t2.t60.t42.t16.t12 a4))
% 0.85/1.04 (step t2.t60.t42.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t16.t4 t2.t60.t42.t16.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t16.t14))
% 0.85/1.04 (step t2.t60.t42.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t16.t14))
% 0.85/1.04 (step t2.t60.t42.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t16.t16 t2.t60.t42.t16.t17))
% 0.85/1.04 (step t2.t60.t42.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t16.t15 t2.t60.t42.t16.t18))
% 0.85/1.04 (step t2.t60.t42.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t42.t16.t19 t2.t60.t42.t16.t20))
% 0.85/1.04 (step t2.t60.t42.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t16.t21 t2.t60.t42.t16.t22))
% 0.85/1.04 (step t2.t60.t42.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t15 t2.t60.t42.t16))
% 0.85/1.04 (step t2.t60.t42.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t19.t4 t2.t60.t42.t19.t5))
% 0.85/1.04 (step t2.t60.t42.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t19.t8.t3 t2.t60.t42.t19.t8.t4))
% 0.85/1.04 (step t2.t60.t42.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t19.t7 t2.t60.t42.t19.t8))
% 0.85/1.04 (step t2.t60.t42.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t19.t6 t2.t60.t42.t19.t9))
% 0.85/1.04 (step t2.t60.t42.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t42.t19.t10 t2.t60.t42.t19.t11))
% 0.85/1.04 (step t2.t60.t42.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t19.t12 t2.t60.t42.t19.t13))
% 0.85/1.04 (step t2.t60.t42.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t19.t14 t2.t60.t42.t19.t15))
% 0.85/1.04 (step t2.t60.t42.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t42.t19.t16 t2.t60.t42.t19.t17))
% 0.85/1.04 (step t2.t60.t42.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t42.t18 t2.t60.t42.t19))
% 0.85/1.04 (step t2.t60.t42.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t17 t2.t60.t42.t20))
% 0.85/1.04 (step t2.t60.t42.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t42.t14 t2.t60.t42.t21 a5))
% 0.85/1.04 (step t2.t60.t42.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t42.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t42.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t25.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t42.t25.t5))
% 0.85/1.04 (step t2.t60.t42.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t42.t25.t5))
% 0.85/1.04 (step t2.t60.t42.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t42.t25.t6 t2.t60.t42.t25.t8))
% 0.85/1.04 (step t2.t60.t42.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t42.t25.t7 t2.t60.t42.t25.t9))
% 0.85/1.04 (step t2.t60.t42.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t42.t25.t6 t2.t60.t42.t25.t11))
% 0.85/1.04 (step t2.t60.t42.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t42.t25.t10 t2.t60.t42.t25.t12))
% 0.85/1.04 (step t2.t60.t42.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t42.t25.t6 t2.t60.t42.t25.t13))
% 0.85/1.04 (step t2.t60.t42.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t25.t14 t2.t60.t42.t25.t15))
% 0.85/1.04 (step t2.t60.t42.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t42.t24 t2.t60.t42.t25))
% 0.85/1.04 (step t2.t60.t42.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t42.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t42.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t42.t28.t5 t2.t60.t42.t28.t6))
% 0.85/1.04 (step t2.t60.t42.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t42.t28.t9.t3 t2.t60.t42.t28.t9.t4))
% 0.85/1.04 (step t2.t60.t42.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t28.t8 t2.t60.t42.t28.t9))
% 0.85/1.04 (step t2.t60.t42.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t42.t28.t7 t2.t60.t42.t28.t10))
% 0.85/1.04 (step t2.t60.t42.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t28.t11 t2.t60.t42.t28.t12))
% 0.85/1.04 (step t2.t60.t42.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t42.t28.t15.t2 t2.t60.t42.t28.t15.t3))
% 0.85/1.04 (step t2.t60.t42.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t28.t14 t2.t60.t42.t28.t15))
% 0.85/1.04 (step t2.t60.t42.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t42.t28.t13 t2.t60.t42.t28.t16))
% 0.85/1.04 (step t2.t60.t42.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t42.t28.t4 t2.t60.t42.t28.t17))
% 0.85/1.04 (step t2.t60.t42.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t42.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t42.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t42.t28.t20.t2))
% 0.85/1.04 (step t2.t60.t42.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t28.t19 t2.t60.t42.t28.t20))
% 0.85/1.04 (step t2.t60.t42.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t42.t28.t18 t2.t60.t42.t28.t21))
% 0.85/1.04 (step t2.t60.t42.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t28.t22 t2.t60.t42.t28.t23))
% 0.85/1.04 (step t2.t60.t42.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t42.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t42.t28.t24 t2.t60.t42.t28.t25))
% 0.85/1.04 (step t2.t60.t42.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t42.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t42.t27 t2.t60.t42.t28))
% 0.85/1.04 (step t2.t60.t42.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t42.t26 t2.t60.t42.t29))
% 0.85/1.04 (step t2.t60.t42.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t42.t23 t2.t60.t42.t30 a4))
% 0.85/1.04 (step t2.t60.t42.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t42.t4 t2.t60.t42.t13 t2.t60.t42.t22 t2.t60.t42.t31 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t42.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t60.t42.t32))
% 0.85/1.04 (step t2.t60.t42.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t60.t42.t32))
% 0.85/1.04 (step t2.t60.t42.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t42.t34 t2.t60.t42.t35))
% 0.85/1.04 (step t2.t60.t42.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t60.t42.t36 t2.t60.t42.t37))
% 0.85/1.04 (step t2.t60.t42.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t60.t42.t33 t2.t60.t42.t38))
% 0.85/1.04 (step t2.t60.t42.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t42.t34 t2.t60.t42.t37))
% 0.85/1.04 (step t2.t60.t42.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t60.t42.t40 t2.t60.t42.t35))
% 0.85/1.04 (step t2.t60.t42.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t60.t42.t39 t2.t60.t42.t41))
% 0.85/1.04 (step t2.t60.t42.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t42.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t60.t42.t42 t2.t60.t42.t43))
% 0.85/1.04 (step t2.t60.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t43 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t60.t41 t2.t60.t42))
% 0.85/1.04 (step t2.t60.t44 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t60.t45.t5 t2.t60.t45.t6))
% 0.85/1.04 (step t2.t60.t45.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t60.t45.t7 t2.t60.t45.t8))
% 0.85/1.04 (step t2.t60.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t45.t4 t2.t60.t45.t9))
% 0.85/1.04 (step t2.t60.t45.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t45.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t45.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t45.t12.t3))
% 0.85/1.04 (step t2.t60.t45.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t60.t45.t12.t4 t2.t60.t45.t12.t5))
% 0.85/1.04 (step t2.t60.t45.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t45.t12.t6))
% 0.85/1.04 (step t2.t60.t45.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t45.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t45.t11 t2.t60.t45.t12))
% 0.85/1.04 (step t2.t60.t45.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t60.t45.t10 t2.t60.t45.t13))
% 0.85/1.04 (step t2.t60.t45.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t60.t45.t15 t2.t60.t45.t16))
% 0.85/1.04 (step t2.t60.t45.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t60.t45.t17 t2.t60.t45.t18))
% 0.85/1.04 (step t2.t60.t45.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t45.t14 t2.t60.t45.t19))
% 0.85/1.04 (step t2.t60.t45.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t45.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t45.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t60.t45.t22.t3))
% 0.85/1.04 (step t2.t60.t45.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t45.t22.t2 t2.t60.t45.t22.t4))
% 0.85/1.04 (step t2.t60.t45.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t60.t45.t22.t5))
% 0.85/1.04 (step t2.t60.t45.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t45.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t45.t21 t2.t60.t45.t22))
% 0.85/1.04 (step t2.t60.t45.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t45.t20 t2.t60.t45.t23))
% 0.85/1.04 (step t2.t60.t45.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t45.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t60.t45.t24 t2.t60.t45.t25))
% 0.85/1.04 (step t2.t60.t45.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t45.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t60.t45.t26 t2.t60.t45.t27))
% 0.85/1.04 (step t2.t60.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t46 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t60.t44 t2.t60.t45))
% 0.85/1.04 (step t2.t60.t47 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t60.t43 t2.t60.t46))
% 0.85/1.04 (step t2.t60.t48 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t60.t40 t2.t60.t47 a7))
% 0.85/1.04 (step t2.t60.t49 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t50 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t51.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t51.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t51.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t51.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t51.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t51.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t51.t7.t7.t5))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t51.t7.t7.t6 t2.t60.t51.t7.t7.t8))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t51.t7.t7.t7 t2.t60.t51.t7.t7.t9))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t51.t7.t7.t6 t2.t60.t51.t7.t7.t11))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t51.t7.t7.t10 t2.t60.t51.t7.t7.t12))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t51.t7.t7.t6 t2.t60.t51.t7.t7.t13))
% 0.85/1.04 (step t2.t60.t51.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t7.t7.t14 t2.t60.t51.t7.t7.t15))
% 0.85/1.04 (step t2.t60.t51.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t51.t7.t6 t2.t60.t51.t7.t7))
% 0.85/1.04 (step t2.t60.t51.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t51.t7.t10.t5 t2.t60.t51.t7.t10.t6))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t51.t7.t10.t9.t3 t2.t60.t51.t7.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t7.t10.t8 t2.t60.t51.t7.t10.t9))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t7.t10.t7 t2.t60.t51.t7.t10.t10))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t51.t7.t10.t11 t2.t60.t51.t7.t10.t12))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t51.t7.t10.t15.t2 t2.t60.t51.t7.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t51.t7.t10.t14 t2.t60.t51.t7.t10.t15))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t51.t7.t10.t13 t2.t60.t51.t7.t10.t16))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t51.t7.t10.t4 t2.t60.t51.t7.t10.t17))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t51.t7.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t51.t7.t10.t19 t2.t60.t51.t7.t10.t20))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t51.t7.t10.t18 t2.t60.t51.t7.t10.t21))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t7.t10.t22 t2.t60.t51.t7.t10.t23))
% 0.85/1.04 (step t2.t60.t51.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t51.t7.t10.t24 t2.t60.t51.t7.t10.t25))
% 0.85/1.04 (step t2.t60.t51.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t51.t7.t9 t2.t60.t51.t7.t10))
% 0.85/1.04 (step t2.t60.t51.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t51.t7.t8 t2.t60.t51.t7.t11))
% 0.85/1.04 (step t2.t60.t51.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t51.t7.t5 t2.t60.t51.t7.t12 a4))
% 0.85/1.04 (step t2.t60.t51.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t51.t7.t4 t2.t60.t51.t7.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t51.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t51.t7.t14))
% 0.85/1.04 (step t2.t60.t51.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t51.t7.t14))
% 0.85/1.04 (step t2.t60.t51.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t51.t7.t16 t2.t60.t51.t7.t17))
% 0.85/1.04 (step t2.t60.t51.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t51.t7.t15 t2.t60.t51.t7.t18))
% 0.85/1.04 (step t2.t60.t51.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t51.t7.t19 t2.t60.t51.t7.t20))
% 0.85/1.04 (step t2.t60.t51.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t7.t21 t2.t60.t51.t7.t22))
% 0.85/1.04 (step t2.t60.t51.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t51.t6 t2.t60.t51.t7))
% 0.85/1.04 (step t2.t60.t51.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t51.t10.t4 t2.t60.t51.t10.t5))
% 0.85/1.04 (step t2.t60.t51.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t51.t10.t8.t3 t2.t60.t51.t10.t8.t4))
% 0.85/1.04 (step t2.t60.t51.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t10.t7 t2.t60.t51.t10.t8))
% 0.85/1.04 (step t2.t60.t51.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t10.t6 t2.t60.t51.t10.t9))
% 0.85/1.04 (step t2.t60.t51.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t51.t10.t10 t2.t60.t51.t10.t11))
% 0.85/1.04 (step t2.t60.t51.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t10.t12 t2.t60.t51.t10.t13))
% 0.85/1.04 (step t2.t60.t51.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t10.t14 t2.t60.t51.t10.t15))
% 0.85/1.04 (step t2.t60.t51.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t51.t10.t16 t2.t60.t51.t10.t17))
% 0.85/1.04 (step t2.t60.t51.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t51.t9 t2.t60.t51.t10))
% 0.85/1.04 (step t2.t60.t51.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t51.t8 t2.t60.t51.t11))
% 0.85/1.04 (step t2.t60.t51.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t51.t5 t2.t60.t51.t12 a5))
% 0.85/1.04 (step t2.t60.t51.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t51.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t51.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t51.t16.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t51.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t51.t16.t5))
% 0.85/1.04 (step t2.t60.t51.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t51.t16.t5))
% 0.85/1.04 (step t2.t60.t51.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t51.t16.t6 t2.t60.t51.t16.t8))
% 0.85/1.04 (step t2.t60.t51.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t51.t16.t7 t2.t60.t51.t16.t9))
% 0.85/1.04 (step t2.t60.t51.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t51.t16.t6 t2.t60.t51.t16.t11))
% 0.85/1.04 (step t2.t60.t51.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t51.t16.t10 t2.t60.t51.t16.t12))
% 0.85/1.04 (step t2.t60.t51.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t51.t16.t6 t2.t60.t51.t16.t13))
% 0.85/1.04 (step t2.t60.t51.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t16.t14 t2.t60.t51.t16.t15))
% 0.85/1.04 (step t2.t60.t51.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t51.t15 t2.t60.t51.t16))
% 0.85/1.04 (step t2.t60.t51.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t51.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t51.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t51.t19.t5 t2.t60.t51.t19.t6))
% 0.85/1.04 (step t2.t60.t51.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t51.t19.t9.t3 t2.t60.t51.t19.t9.t4))
% 0.85/1.04 (step t2.t60.t51.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t19.t8 t2.t60.t51.t19.t9))
% 0.85/1.04 (step t2.t60.t51.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t51.t19.t7 t2.t60.t51.t19.t10))
% 0.85/1.04 (step t2.t60.t51.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t51.t19.t11 t2.t60.t51.t19.t12))
% 0.85/1.04 (step t2.t60.t51.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t51.t19.t15.t2 t2.t60.t51.t19.t15.t3))
% 0.85/1.04 (step t2.t60.t51.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t51.t19.t14 t2.t60.t51.t19.t15))
% 0.85/1.04 (step t2.t60.t51.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t51.t19.t13 t2.t60.t51.t19.t16))
% 0.85/1.04 (step t2.t60.t51.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t51.t19.t4 t2.t60.t51.t19.t17))
% 0.85/1.04 (step t2.t60.t51.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t51.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t51.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t51.t19.t20.t2))
% 0.85/1.04 (step t2.t60.t51.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t51.t19.t19 t2.t60.t51.t19.t20))
% 0.85/1.04 (step t2.t60.t51.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t51.t19.t18 t2.t60.t51.t19.t21))
% 0.85/1.04 (step t2.t60.t51.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t19.t22 t2.t60.t51.t19.t23))
% 0.85/1.04 (step t2.t60.t51.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t51.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t51.t19.t24 t2.t60.t51.t19.t25))
% 0.85/1.04 (step t2.t60.t51.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t51.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t51.t18 t2.t60.t51.t19))
% 0.85/1.04 (step t2.t60.t51.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t51.t17 t2.t60.t51.t20))
% 0.85/1.04 (step t2.t60.t51.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t51.t14 t2.t60.t51.t21 a4))
% 0.85/1.04 (step t2.t60.t51.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t51.t4 t2.t60.t51.t13 t2.t60.t51.t22 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t51.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t51.t23))
% 0.85/1.04 (step t2.t60.t51.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t51.t23))
% 0.85/1.04 (step t2.t60.t51.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t51.t25 t2.t60.t51.t26))
% 0.85/1.04 (step t2.t60.t51.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t51.t24 t2.t60.t51.t27))
% 0.85/1.04 (step t2.t60.t51.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t60.t51.t28 t2.t60.t51.t29))
% 0.85/1.04 (step t2.t60.t51.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t51.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t60.t51.t30 t2.t60.t51.t31))
% 0.85/1.04 (step t2.t60.t51 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t52 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t60.t50 t2.t60.t51))
% 0.85/1.04 (step t2.t60.t53 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t54 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t54.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t54.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t54.t4 t2.t60.t54.t5))
% 0.85/1.04 (step t2.t60.t54.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t54.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t54.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t54.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t54.t8.t3 t2.t60.t54.t8.t4))
% 0.85/1.04 (step t2.t60.t54.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t54.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t54.t7 t2.t60.t54.t8))
% 0.85/1.04 (step t2.t60.t54.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t54.t6 t2.t60.t54.t9))
% 0.85/1.04 (step t2.t60.t54.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t60.t54.t10 t2.t60.t54.t11))
% 0.85/1.04 (step t2.t60.t54.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t54.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t60.t54.t12 t2.t60.t54.t13))
% 0.85/1.04 (step t2.t60.t54.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t54.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t54.t14 t2.t60.t54.t15))
% 0.85/1.04 (step t2.t60.t54.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t54.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t60.t54.t16 t2.t60.t54.t17))
% 0.85/1.04 (step t2.t60.t54 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t55 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t60.t53 t2.t60.t54))
% 0.85/1.04 (step t2.t60.t56 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t60.t52 t2.t60.t55))
% 0.85/1.04 (step t2.t60.t57 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t60.t49 t2.t60.t56 a6))
% 0.85/1.04 (step t2.t60.t58 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t59 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t60 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t60.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t60.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t60.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t60.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t60.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t60.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t60.t7.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t60.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t60.t7.t5))
% 0.85/1.04 (step t2.t60.t60.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t60.t7.t5))
% 0.85/1.04 (step t2.t60.t60.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t60.t7.t6 t2.t60.t60.t7.t8))
% 0.85/1.04 (step t2.t60.t60.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t60.t7.t7 t2.t60.t60.t7.t9))
% 0.85/1.04 (step t2.t60.t60.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t60.t7.t6 t2.t60.t60.t7.t11))
% 0.85/1.04 (step t2.t60.t60.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t60.t7.t10 t2.t60.t60.t7.t12))
% 0.85/1.04 (step t2.t60.t60.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t60.t7.t6 t2.t60.t60.t7.t13))
% 0.85/1.04 (step t2.t60.t60.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t60.t7.t14 t2.t60.t60.t7.t15))
% 0.85/1.04 (step t2.t60.t60.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t60.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t60.t6 t2.t60.t60.t7))
% 0.85/1.04 (step t2.t60.t60.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t60.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t60.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t60.t10.t5 t2.t60.t60.t10.t6))
% 0.85/1.04 (step t2.t60.t60.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t60.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t60.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t60.t10.t9.t3 t2.t60.t60.t10.t9.t4))
% 0.85/1.04 (step t2.t60.t60.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t60.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t60.t10.t8 t2.t60.t60.t10.t9))
% 0.85/1.04 (step t2.t60.t60.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t60.t10.t7 t2.t60.t60.t10.t10))
% 0.85/1.04 (step t2.t60.t60.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t60.t10.t11 t2.t60.t60.t10.t12))
% 0.85/1.04 (step t2.t60.t60.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t60.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t60.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t60.t10.t15.t2 t2.t60.t60.t10.t15.t3))
% 0.85/1.04 (step t2.t60.t60.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t60.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t60.t10.t14 t2.t60.t60.t10.t15))
% 0.85/1.04 (step t2.t60.t60.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t60.t10.t13 t2.t60.t60.t10.t16))
% 0.85/1.04 (step t2.t60.t60.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t60.t10.t4 t2.t60.t60.t10.t17))
% 0.85/1.04 (step t2.t60.t60.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t60.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t60.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t60.t10.t20.t2))
% 0.85/1.04 (step t2.t60.t60.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t60.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t60.t10.t19 t2.t60.t60.t10.t20))
% 0.85/1.04 (step t2.t60.t60.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t60.t10.t18 t2.t60.t60.t10.t21))
% 0.85/1.04 (step t2.t60.t60.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t60.t10.t22 t2.t60.t60.t10.t23))
% 0.85/1.04 (step t2.t60.t60.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t60.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t60.t10.t24 t2.t60.t60.t10.t25))
% 0.85/1.04 (step t2.t60.t60.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t60.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t60.t9 t2.t60.t60.t10))
% 0.85/1.04 (step t2.t60.t60.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t60.t8 t2.t60.t60.t11))
% 0.85/1.04 (step t2.t60.t60.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t60.t5 t2.t60.t60.t12 a4))
% 0.85/1.04 (step t2.t60.t60.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t60.t4 t2.t60.t60.t13 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t60.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t60.t14))
% 0.85/1.04 (step t2.t60.t60.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t60.t14))
% 0.85/1.04 (step t2.t60.t60.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t60.t16 t2.t60.t60.t17))
% 0.85/1.04 (step t2.t60.t60.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t60.t15 t2.t60.t60.t18))
% 0.85/1.04 (step t2.t60.t60.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t60.t60.t19 t2.t60.t60.t20))
% 0.85/1.04 (step t2.t60.t60.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t60.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t60.t60.t21 t2.t60.t60.t22))
% 0.85/1.04 (step t2.t60.t60 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t61 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t60.t59 t2.t60.t60))
% 0.85/1.04 (step t2.t60.t62 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t63 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t63.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t63.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t63.t4 t2.t60.t63.t5))
% 0.85/1.04 (step t2.t60.t63.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t63.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t63.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t63.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t63.t8.t3 t2.t60.t63.t8.t4))
% 0.85/1.04 (step t2.t60.t63.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t63.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t63.t7 t2.t60.t63.t8))
% 0.85/1.04 (step t2.t60.t63.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t63.t6 t2.t60.t63.t9))
% 0.85/1.04 (step t2.t60.t63.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t60.t63.t10 t2.t60.t63.t11))
% 0.85/1.04 (step t2.t60.t63.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t63.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t63.t12 t2.t60.t63.t13))
% 0.85/1.04 (step t2.t60.t63.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t63.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t60.t63.t14 t2.t60.t63.t15))
% 0.85/1.04 (step t2.t60.t63.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t63.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t60.t63.t16 t2.t60.t63.t17))
% 0.85/1.04 (step t2.t60.t63 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.04 (step t2.t60.t64 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t60.t62 t2.t60.t63))
% 0.85/1.04 (step t2.t60.t65 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t61 t2.t60.t64))
% 0.85/1.04 (step t2.t60.t66 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t60.t58 t2.t60.t65 a5))
% 0.85/1.04 (step t2.t60.t67 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.04 (step t2.t60.t68 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t69 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t69.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.04 (step t2.t60.t69.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t69.t4 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t69.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t69.t5))
% 0.85/1.04 (step t2.t60.t69.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t60.t69.t5))
% 0.85/1.04 (step t2.t60.t69.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t69.t6 t2.t60.t69.t8))
% 0.85/1.04 (step t2.t60.t69.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t69.t7 t2.t60.t69.t9))
% 0.85/1.04 (step t2.t60.t69.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t60.t69.t6 t2.t60.t69.t11))
% 0.85/1.04 (step t2.t60.t69.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t60.t69.t10 t2.t60.t69.t12))
% 0.85/1.04 (step t2.t60.t69.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t60.t69.t6 t2.t60.t69.t13))
% 0.85/1.04 (step t2.t60.t69.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t69.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t60.t69.t14 t2.t60.t69.t15))
% 0.85/1.04 (step t2.t60.t69 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.04 (step t2.t60.t70 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t60.t68 t2.t60.t69))
% 0.85/1.04 (step t2.t60.t71 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.04 (anchor :step t2.t60.t72 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.04 (step t2.t60.t72.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t60.t72.t5 t2.t60.t72.t6))
% 0.85/1.04 (step t2.t60.t72.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t72.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t72.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t60.t72.t9.t3 t2.t60.t72.t9.t4))
% 0.85/1.04 (step t2.t60.t72.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.04 (step t2.t60.t72.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t72.t8 t2.t60.t72.t9))
% 0.85/1.04 (step t2.t60.t72.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t60.t72.t7 t2.t60.t72.t10))
% 0.85/1.04 (step t2.t60.t72.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t72.t11 t2.t60.t72.t12))
% 0.85/1.04 (step t2.t60.t72.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t72.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t72.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t60.t72.t15.t2 t2.t60.t72.t15.t3))
% 0.85/1.04 (step t2.t60.t72.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.04 (step t2.t60.t72.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t72.t14 t2.t60.t72.t15))
% 0.85/1.04 (step t2.t60.t72.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t60.t72.t13 t2.t60.t72.t16))
% 0.85/1.04 (step t2.t60.t72.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t60.t72.t4 t2.t60.t72.t17))
% 0.85/1.04 (step t2.t60.t72.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t72.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t72.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t60.t72.t20.t2))
% 0.85/1.04 (step t2.t60.t72.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t72.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t72.t19 t2.t60.t72.t20))
% 0.85/1.04 (step t2.t60.t72.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t60.t72.t18 t2.t60.t72.t21))
% 0.85/1.04 (step t2.t60.t72.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.04 (step t2.t60.t72.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t60.t72.t22 t2.t60.t72.t23))
% 0.85/1.04 (step t2.t60.t72.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t72.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t60.t72.t24 t2.t60.t72.t25))
% 0.85/1.04 (step t2.t60.t72 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.04 (step t2.t60.t73 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t60.t71 t2.t60.t72))
% 0.85/1.04 (step t2.t60.t74 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t60.t70 t2.t60.t73))
% 0.85/1.04 (step t2.t60.t75 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t60.t67 t2.t60.t74 a4))
% 0.85/1.04 (step t2.t60.t76 (cl (and (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t7 t2.t60.t12 t2.t60.t21 t2.t60.t30 a10 a9 t2.t60.t39 t2.t60.t48 t2.t60.t57 t2.t60.t66 t2.t60.t75 a3 a2 a1 a0))
% 0.85/1.04 (step t2.t60.t77 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t76))
% 0.85/1.04 (step t2.t60.t78 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule and :premises (t2.t60.t76))
% 0.85/1.04 (step t2.t60.t79 (cl (= (@ tptp.mnot tptp.mtrue) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) :rule cong :premises (t2.t60.t77 t2.t60.t78))
% 0.85/1.04 (step t2.t60.t80 (cl (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))))) :rule cong :premises (t2.t60.t6 t2.t60.t79))
% 0.85/1.04 (step t2.t60.t81 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.85/1.04 (step t2.t60.t82 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))))) :rule all_simplify)
% 0.85/1.04 (anchor :step t2.t60.t83 :args ((W $$unsorted) (:= W W)))
% 0.85/1.04 (step t2.t60.t83.t1 (cl (= W W)) :rule refl)
% 0.85/1.04 (step t2.t60.t83.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W) true)) :rule all_simplify)
% 0.85/1.04 (step t2.t60.t83.t3 (cl (= (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) (not true))) :rule cong :premises (t2.t60.t83.t2))
% 0.85/1.05 (step t2.t60.t83.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.85/1.05 (step t2.t60.t83.t5 (cl (= (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) false)) :rule trans :premises (t2.t60.t83.t3 t2.t60.t83.t4))
% 0.85/1.05 (step t2.t60.t83 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))) (lambda ((W $$unsorted)) false))) :rule bind)
% 0.85/1.05 (step t2.t60.t84 (cl (= (lambda ((W $$unsorted)) false) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule all_simplify)
% 0.85/1.05 (step t2.t60.t85 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule trans :premises (t2.t60.t83 t2.t60.t84))
% 0.85/1.05 (step t2.t60.t86 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule trans :premises (t2.t60.t82 t2.t60.t85))
% 0.85/1.05 (step t2.t60.t87 (cl (= (= tptp.mfalse (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) :rule cong :premises (t2.t60.t81 t2.t60.t86))
% 0.85/1.05 (step t2.t60.t88 (cl (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) :rule trans :premises (t2.t60.t80 t2.t60.t87))
% 0.85/1.05 (step t2.t60.t89 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule resolution :premises (t2.t60.t5 t2.t60.t88 a14))
% 0.85/1.05 (step t2.t60.t90 (cl (and (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t60.t4 a15 t2.t60.t89 t2.t60.t12 t2.t60.t21 t2.t60.t30 a10 a9 t2.t60.t39 t2.t60.t48 t2.t60.t57 t2.t60.t66 t2.t60.t75 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t60.t91 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t60.t90))
% 0.85/1.05 (step t2.t60.t92 (cl (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) :rule and :premises (t2.t60.t90))
% 0.85/1.05 (step t2.t60.t93 (cl (= R R)) :rule refl)
% 0.85/1.05 (step t2.t60.t94 (cl (= (@ tptp.mbox R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R))) :rule cong :premises (t2.t60.t92 t2.t60.t93))
% 0.85/1.05 (step t2.t60.t95 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t60.t96 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t60.t91 t2.t60.t95))
% 0.85/1.05 (step t2.t60.t97 (cl (= (@ (@ tptp.mbox R) (@ tptp.mnot Phi)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t60.t94 t2.t60.t96))
% 0.85/1.05 (step t2.t60.t98 (cl (= (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))))) :rule cong :premises (t2.t60.t91 t2.t60.t97))
% 0.85/1.05 (step t2.t60.t99 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t60.t100 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0))) :rule cong :premises (t2.t60.t98 t2.t60.t99))
% 0.85/1.05 (step t2.t60 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0)) (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t61 (cl (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0))))) :rule cong :premises (t2.t59 t2.t60))
% 0.85/1.05 (step t2.t62 (cl (= tptp.mdia tptp.mdia)) :rule refl)
% 0.85/1.05 (anchor :step t2.t63 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (Phi (-> $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t63.t1 (cl (= R R)) :rule refl)
% 0.85/1.05 (step t2.t63.t2 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t63.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t63.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t63.t5 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t63.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t63.t7 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t63.t5 t2.t63.t6))
% 0.85/1.05 (step t2.t63.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((W $$unsorted)) (not (@ Phi W))) V)))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t63.t9 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t63.t9.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (anchor :step t2.t63.t9.t2 :args ((V $$unsorted) (:= V V)))
% 0.85/1.05 (step t2.t63.t9.t2.t1 (cl (= V V)) :rule refl)
% 0.85/1.05 (step t2.t63.t9.t2.t2 (cl (= (not (@ (@ R W) V)) (not (@ (@ R W) V)))) :rule refl)
% 0.85/1.05 (step t2.t63.t9.t2.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) V) (not (@ Phi V)))) :rule all_simplify)
% 0.85/1.05 (step t2.t63.t9.t2.t4 (cl (= (or (not (@ (@ R W) V)) (@ (lambda ((W $$unsorted)) (not (@ Phi W))) V)) (or (not (@ (@ R W) V)) (not (@ Phi V))))) :rule cong :premises (t2.t63.t9.t2.t2 t2.t63.t9.t2.t3))
% 0.85/1.05 (step t2.t63.t9.t2 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((W $$unsorted)) (not (@ Phi W))) V))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) :rule bind)
% 0.85/1.05 (step t2.t63.t9 (cl (= (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((W $$unsorted)) (not (@ Phi W))) V)))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))))) :rule bind)
% 0.85/1.05 (step t2.t63.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))))) :rule trans :premises (t2.t63.t8 t2.t63.t9))
% 0.85/1.05 (step t2.t63.t11 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))))) :rule trans :premises (t2.t63.t7 t2.t63.t10))
% 0.85/1.05 (step t2.t63.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))))) :rule cong :premises (t2.t63.t4 t2.t63.t11))
% 0.85/1.05 (step t2.t63.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t63.t14 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t63.t14.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t63.t14.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))) W) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t63.t14.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))) W)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))))) :rule cong :premises (t2.t63.t14.t2))
% 0.85/1.05 (step t2.t63.t14 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V))))) W))) (lambda ((W $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))))) :rule bind)
% 0.85/1.05 (step t2.t63.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) (lambda ((W $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))))) :rule trans :premises (t2.t63.t13 t2.t63.t14))
% 0.85/1.05 (step t2.t63.t16 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) (lambda ((W $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))))) :rule trans :premises (t2.t63.t12 t2.t63.t15))
% 0.85/1.05 (step t2.t63.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t63.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) __flatten_var_0))) :rule cong :premises (t2.t63.t16 t2.t63.t17))
% 0.85/1.05 (step t2.t63.t19 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (not (@ Phi V)))))) __flatten_var_0) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t63.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))) :rule trans :premises (t2.t63.t18 t2.t63.t19))
% 0.85/1.05 (step t2.t63 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0)) (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V)))))))) :rule bind)
% 0.85/1.05 (step t2.t64 (cl (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) __flatten_var_0))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))))) :rule cong :premises (t2.t62 t2.t63))
% 0.85/1.05 (step t2.t65 (cl (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))))) :rule trans :premises (t2.t61 t2.t64))
% 0.85/1.05 (step t2.t66 (cl (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V)))))))) :rule resolution :premises (t2.t58 t2.t65 a16))
% 0.85/1.05 (step t2.t67 (cl (not (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) (not (= tptp.mfalse (@ tptp.mnot tptp.mtrue))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t68 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.85/1.05 (step t2.t69 (cl (and (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t70 (cl (not (= (= tptp.mtrue (lambda ((W $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((W $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t71 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.85/1.05 (step t2.t72 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule all_simplify)
% 0.85/1.05 (step t2.t73 (cl (= (= tptp.mtrue (lambda ((W $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) :rule cong :premises (t2.t71 t2.t72))
% 0.85/1.05 (step t2.t74 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule resolution :premises (t2.t70 t2.t73 a13))
% 0.85/1.05 (step t2.t75 (cl (not (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) (not (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t76 (cl (= tptp.mexists_prop tptp.mexists_prop)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77 :args ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t3 (cl (and (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t4 (cl (not (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t5 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t3 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t4 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t5 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t6 t2.t77.t6.t6.t7.t7.t7.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t7 t2.t77.t6.t6.t7.t7.t7.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t6 t2.t77.t6.t6.t7.t7.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t10 t2.t77.t6.t6.t7.t7.t7.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t6 t2.t77.t6.t6.t7.t7.t7.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t7.t14 t2.t77.t6.t6.t7.t7.t7.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t6 t2.t77.t6.t6.t7.t7.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t5 t2.t77.t6.t6.t7.t7.t7.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t9.t3 t2.t77.t6.t6.t7.t7.t7.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t8 t2.t77.t6.t6.t7.t7.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t7 t2.t77.t6.t6.t7.t7.t7.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t11 t2.t77.t6.t6.t7.t7.t7.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t15.t2 t2.t77.t6.t6.t7.t7.t7.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t14 t2.t77.t6.t6.t7.t7.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t13 t2.t77.t6.t6.t7.t7.t7.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t4 t2.t77.t6.t6.t7.t7.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t19 t2.t77.t6.t6.t7.t7.t7.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t18 t2.t77.t6.t6.t7.t7.t7.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t10.t22 t2.t77.t6.t6.t7.t7.t7.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t10.t24 t2.t77.t6.t6.t7.t7.t7.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t9 t2.t77.t6.t6.t7.t7.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t7.t8 t2.t77.t6.t6.t7.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t7.t5 t2.t77.t6.t6.t7.t7.t7.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t7.t4 t2.t77.t6.t6.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t16 t2.t77.t6.t6.t7.t7.t7.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t15 t2.t77.t6.t6.t7.t7.t7.t18))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t19 t2.t77.t6.t6.t7.t7.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t7.t21 t2.t77.t6.t6.t7.t7.t7.t22))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t6 t2.t77.t6.t6.t7.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t10.t4 t2.t77.t6.t6.t7.t7.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t10.t8.t3 t2.t77.t6.t6.t7.t7.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t10.t7 t2.t77.t6.t6.t7.t7.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t10.t6 t2.t77.t6.t6.t7.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t10.t10 t2.t77.t6.t6.t7.t7.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t10.t12 t2.t77.t6.t6.t7.t7.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t10.t14 t2.t77.t6.t6.t7.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t10.t16 t2.t77.t6.t6.t7.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t9 t2.t77.t6.t6.t7.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t8 t2.t77.t6.t6.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t5 t2.t77.t6.t6.t7.t7.t12 a5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t6 t2.t77.t6.t6.t7.t7.t16.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t7 t2.t77.t6.t6.t7.t7.t16.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t6 t2.t77.t6.t6.t7.t7.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t10 t2.t77.t6.t6.t7.t7.t16.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t6 t2.t77.t6.t6.t7.t7.t16.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t16.t14 t2.t77.t6.t6.t7.t7.t16.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t15 t2.t77.t6.t6.t7.t7.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t5 t2.t77.t6.t6.t7.t7.t19.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t9.t3 t2.t77.t6.t6.t7.t7.t19.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t8 t2.t77.t6.t6.t7.t7.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t7 t2.t77.t6.t6.t7.t7.t19.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t11 t2.t77.t6.t6.t7.t7.t19.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t15.t2 t2.t77.t6.t6.t7.t7.t19.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t14 t2.t77.t6.t6.t7.t7.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t13 t2.t77.t6.t6.t7.t7.t19.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t4 t2.t77.t6.t6.t7.t7.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t19 t2.t77.t6.t6.t7.t7.t19.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t18 t2.t77.t6.t6.t7.t7.t19.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t19.t22 t2.t77.t6.t6.t7.t7.t19.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t19.t24 t2.t77.t6.t6.t7.t7.t19.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t18 t2.t77.t6.t6.t7.t7.t19))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t7.t7.t17 t2.t77.t6.t6.t7.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t14 t2.t77.t6.t6.t7.t7.t21 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t7.t4 t2.t77.t6.t6.t7.t7.t13 t2.t77.t6.t6.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t7.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t25 t2.t77.t6.t6.t7.t7.t26))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t24 t2.t77.t6.t6.t7.t7.t27))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t28 t2.t77.t6.t6.t7.t7.t29))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t7.t30 t2.t77.t6.t6.t7.t7.t31))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t6 t2.t77.t6.t6.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t10.t4 t2.t77.t6.t6.t7.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t10.t8.t3 t2.t77.t6.t6.t7.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t10.t7 t2.t77.t6.t6.t7.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t10.t6 t2.t77.t6.t6.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t10.t10 t2.t77.t6.t6.t7.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t10.t12 t2.t77.t6.t6.t7.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t10.t14 t2.t77.t6.t6.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t7.t10.t16 t2.t77.t6.t6.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t7.t9 t2.t77.t6.t6.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t8 t2.t77.t6.t6.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t7.t5 t2.t77.t6.t6.t7.t12 a6))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t16.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t16.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t6 t2.t77.t6.t6.t7.t16.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t7 t2.t77.t6.t6.t7.t16.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t6 t2.t77.t6.t6.t7.t16.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t10 t2.t77.t6.t6.t7.t16.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t6 t2.t77.t6.t6.t7.t16.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t7.t14 t2.t77.t6.t6.t7.t16.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t6 t2.t77.t6.t6.t7.t16.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t5 t2.t77.t6.t6.t7.t16.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t9.t3 t2.t77.t6.t6.t7.t16.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t8 t2.t77.t6.t6.t7.t16.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t7 t2.t77.t6.t6.t7.t16.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t11 t2.t77.t6.t6.t7.t16.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t15.t2 t2.t77.t6.t6.t7.t16.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t14 t2.t77.t6.t6.t7.t16.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t13 t2.t77.t6.t6.t7.t16.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t4 t2.t77.t6.t6.t7.t16.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t19 t2.t77.t6.t6.t7.t16.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t18 t2.t77.t6.t6.t7.t16.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t10.t22 t2.t77.t6.t6.t7.t16.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t10.t24 t2.t77.t6.t6.t7.t16.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t9 t2.t77.t6.t6.t7.t16.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t7.t16.t8 t2.t77.t6.t6.t7.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t7.t16.t5 t2.t77.t6.t6.t7.t16.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t16.t4 t2.t77.t6.t6.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t16.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t16.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t16 t2.t77.t6.t6.t7.t16.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t15 t2.t77.t6.t6.t7.t16.t18))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t19 t2.t77.t6.t6.t7.t16.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t16.t21 t2.t77.t6.t6.t7.t16.t22))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t15 t2.t77.t6.t6.t7.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t19.t4 t2.t77.t6.t6.t7.t19.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t19.t8.t3 t2.t77.t6.t6.t7.t19.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t19.t7 t2.t77.t6.t6.t7.t19.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t19.t6 t2.t77.t6.t6.t7.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t19.t10 t2.t77.t6.t6.t7.t19.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t19.t12 t2.t77.t6.t6.t7.t19.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t19.t14 t2.t77.t6.t6.t7.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t7.t19.t16 t2.t77.t6.t6.t7.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t7.t18 t2.t77.t6.t6.t7.t19))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t17 t2.t77.t6.t6.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t7.t14 t2.t77.t6.t6.t7.t21 a5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t7.t25.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t7.t25.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t6 t2.t77.t6.t6.t7.t25.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t7 t2.t77.t6.t6.t7.t25.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t6 t2.t77.t6.t6.t7.t25.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t10 t2.t77.t6.t6.t7.t25.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t6 t2.t77.t6.t6.t7.t25.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t25.t14 t2.t77.t6.t6.t7.t25.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t7.t24 t2.t77.t6.t6.t7.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t5 t2.t77.t6.t6.t7.t28.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t9.t3 t2.t77.t6.t6.t7.t28.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t8 t2.t77.t6.t6.t7.t28.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t7 t2.t77.t6.t6.t7.t28.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t11 t2.t77.t6.t6.t7.t28.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t15.t2 t2.t77.t6.t6.t7.t28.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t14 t2.t77.t6.t6.t7.t28.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t13 t2.t77.t6.t6.t7.t28.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t4 t2.t77.t6.t6.t7.t28.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t19 t2.t77.t6.t6.t7.t28.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t18 t2.t77.t6.t6.t7.t28.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t28.t22 t2.t77.t6.t6.t7.t28.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t7.t28.t24 t2.t77.t6.t6.t7.t28.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t7.t27 t2.t77.t6.t6.t7.t28))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t7.t26 t2.t77.t6.t6.t7.t29))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t7.t23 t2.t77.t6.t6.t7.t30 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t7.t4 t2.t77.t6.t6.t7.t13 t2.t77.t6.t6.t7.t22 t2.t77.t6.t6.t7.t31 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t77.t6.t6.t7.t32))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t77.t6.t6.t7.t32))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t34 t2.t77.t6.t6.t7.t35))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t36 t2.t77.t6.t6.t7.t37))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t77.t6.t6.t7.t33 t2.t77.t6.t6.t7.t38))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t6.t6.t7.t34 t2.t77.t6.t6.t7.t37))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t77.t6.t6.t7.t40 t2.t77.t6.t6.t7.t35))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t77.t6.t6.t7.t39 t2.t77.t6.t6.t7.t41))
% 0.85/1.05 (step t2.t77.t6.t6.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t7.t42 t2.t77.t6.t6.t7.t43))
% 0.85/1.05 (step t2.t77.t6.t6.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t6 t2.t77.t6.t6.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t6.t6.t10.t5 t2.t77.t6.t6.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t77.t6.t6.t10.t7 t2.t77.t6.t6.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t10.t4 t2.t77.t6.t6.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t10.t12.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t10.t12.t4 t2.t77.t6.t6.t10.t12.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t10.t12.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t6.t10.t11 t2.t77.t6.t6.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t6.t10.t10 t2.t77.t6.t6.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t6.t6.t10.t15 t2.t77.t6.t6.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t77.t6.t6.t10.t17 t2.t77.t6.t6.t10.t18))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t10.t14 t2.t77.t6.t6.t10.t19))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t10.t22.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t10.t22.t2 t2.t77.t6.t6.t10.t22.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t77.t6.t6.t10.t22.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t10.t21 t2.t77.t6.t6.t10.t22))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t10.t20 t2.t77.t6.t6.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t10.t24 t2.t77.t6.t6.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t6.t10.t26 t2.t77.t6.t6.t10.t27))
% 0.85/1.05 (step t2.t77.t6.t6.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t6.t6.t9 t2.t77.t6.t6.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t77.t6.t6.t8 t2.t77.t6.t6.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t77.t6.t6.t5 t2.t77.t6.t6.t12 a7))
% 0.85/1.05 (step t2.t77.t6.t6.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t16.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t16.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t6 t2.t77.t6.t6.t16.t7.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t7 t2.t77.t6.t6.t16.t7.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t6 t2.t77.t6.t6.t16.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t10 t2.t77.t6.t6.t16.t7.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t6 t2.t77.t6.t6.t16.t7.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t7.t14 t2.t77.t6.t6.t16.t7.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t6 t2.t77.t6.t6.t16.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t5 t2.t77.t6.t6.t16.t7.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t9.t3 t2.t77.t6.t6.t16.t7.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t8 t2.t77.t6.t6.t16.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t7 t2.t77.t6.t6.t16.t7.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t11 t2.t77.t6.t6.t16.t7.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t15.t2 t2.t77.t6.t6.t16.t7.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t14 t2.t77.t6.t6.t16.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t13 t2.t77.t6.t6.t16.t7.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t4 t2.t77.t6.t6.t16.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t19 t2.t77.t6.t6.t16.t7.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t18 t2.t77.t6.t6.t16.t7.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t10.t22 t2.t77.t6.t6.t16.t7.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t10.t24 t2.t77.t6.t6.t16.t7.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t9 t2.t77.t6.t6.t16.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t16.t7.t8 t2.t77.t6.t6.t16.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t16.t7.t5 t2.t77.t6.t6.t16.t7.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t16.t7.t4 t2.t77.t6.t6.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t16.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t16.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t16 t2.t77.t6.t6.t16.t7.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t15 t2.t77.t6.t6.t16.t7.t18))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t19 t2.t77.t6.t6.t16.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t7.t21 t2.t77.t6.t6.t16.t7.t22))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t16.t6 t2.t77.t6.t6.t16.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t10.t4 t2.t77.t6.t6.t16.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t16.t10.t8.t3 t2.t77.t6.t6.t16.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t10.t7 t2.t77.t6.t6.t16.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t10.t6 t2.t77.t6.t6.t16.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t16.t10.t10 t2.t77.t6.t6.t16.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t10.t12 t2.t77.t6.t6.t16.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t10.t14 t2.t77.t6.t6.t16.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t16.t10.t16 t2.t77.t6.t6.t16.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t16.t9 t2.t77.t6.t6.t16.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t16.t8 t2.t77.t6.t6.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t16.t5 t2.t77.t6.t6.t16.t12 a5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t16.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t16.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t6 t2.t77.t6.t6.t16.t16.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t7 t2.t77.t6.t6.t16.t16.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t6 t2.t77.t6.t6.t16.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t10 t2.t77.t6.t6.t16.t16.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t6 t2.t77.t6.t6.t16.t16.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t16.t14 t2.t77.t6.t6.t16.t16.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t16.t15 t2.t77.t6.t6.t16.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t5 t2.t77.t6.t6.t16.t19.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t9.t3 t2.t77.t6.t6.t16.t19.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t8 t2.t77.t6.t6.t16.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t7 t2.t77.t6.t6.t16.t19.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t11 t2.t77.t6.t6.t16.t19.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t15.t2 t2.t77.t6.t6.t16.t19.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t14 t2.t77.t6.t6.t16.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t13 t2.t77.t6.t6.t16.t19.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t4 t2.t77.t6.t6.t16.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t19 t2.t77.t6.t6.t16.t19.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t18 t2.t77.t6.t6.t16.t19.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t19.t22 t2.t77.t6.t6.t16.t19.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t16.t19.t24 t2.t77.t6.t6.t16.t19.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t16.t18 t2.t77.t6.t6.t16.t19))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t16.t17 t2.t77.t6.t6.t16.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t16.t14 t2.t77.t6.t6.t16.t21 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t16.t4 t2.t77.t6.t6.t16.t13 t2.t77.t6.t6.t16.t22 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t16.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t16.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t16.t25 t2.t77.t6.t6.t16.t26))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t16.t24 t2.t77.t6.t6.t16.t27))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t6.t6.t16.t28 t2.t77.t6.t6.t16.t29))
% 0.85/1.05 (step t2.t77.t6.t6.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t16.t30 t2.t77.t6.t6.t16.t31))
% 0.85/1.05 (step t2.t77.t6.t6.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t15 t2.t77.t6.t6.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t19.t4 t2.t77.t6.t6.t19.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t19.t8.t3 t2.t77.t6.t6.t19.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t19.t7 t2.t77.t6.t6.t19.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t19.t6 t2.t77.t6.t6.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t19.t10 t2.t77.t6.t6.t19.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t6.t6.t19.t12 t2.t77.t6.t6.t19.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t19.t14 t2.t77.t6.t6.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t19.t16 t2.t77.t6.t6.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t18 t2.t77.t6.t6.t19))
% 0.85/1.05 (step t2.t77.t6.t6.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t17 t2.t77.t6.t6.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t14 t2.t77.t6.t6.t21 a6))
% 0.85/1.05 (step t2.t77.t6.t6.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t25.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t25.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t6 t2.t77.t6.t6.t25.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t7 t2.t77.t6.t6.t25.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t6 t2.t77.t6.t6.t25.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t10 t2.t77.t6.t6.t25.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t6 t2.t77.t6.t6.t25.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t25.t7.t14 t2.t77.t6.t6.t25.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t25.t6 t2.t77.t6.t6.t25.t7))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t5 t2.t77.t6.t6.t25.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t9.t3 t2.t77.t6.t6.t25.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t8 t2.t77.t6.t6.t25.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t7 t2.t77.t6.t6.t25.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t11 t2.t77.t6.t6.t25.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t15.t2 t2.t77.t6.t6.t25.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t14 t2.t77.t6.t6.t25.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t13 t2.t77.t6.t6.t25.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t4 t2.t77.t6.t6.t25.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t19 t2.t77.t6.t6.t25.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t18 t2.t77.t6.t6.t25.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t25.t10.t22 t2.t77.t6.t6.t25.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t25.t10.t24 t2.t77.t6.t6.t25.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t25.t9 t2.t77.t6.t6.t25.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t25.t8 t2.t77.t6.t6.t25.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t25.t5 t2.t77.t6.t6.t25.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t25.t4 t2.t77.t6.t6.t25.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t25.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t25.t14))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t25.t16 t2.t77.t6.t6.t25.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t25.t15 t2.t77.t6.t6.t25.t18))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t6.t25.t19 t2.t77.t6.t6.t25.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t25.t21 t2.t77.t6.t6.t25.t22))
% 0.85/1.05 (step t2.t77.t6.t6.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t24 t2.t77.t6.t6.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t28.t4 t2.t77.t6.t6.t28.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t28.t8.t3 t2.t77.t6.t6.t28.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t28.t7 t2.t77.t6.t6.t28.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t28.t6 t2.t77.t6.t6.t28.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t28.t10 t2.t77.t6.t6.t28.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t28.t12 t2.t77.t6.t6.t28.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t28.t14 t2.t77.t6.t6.t28.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t6.t28.t16 t2.t77.t6.t6.t28.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t6.t27 t2.t77.t6.t6.t28))
% 0.85/1.05 (step t2.t77.t6.t6.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t26 t2.t77.t6.t6.t29))
% 0.85/1.05 (step t2.t77.t6.t6.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t6.t23 t2.t77.t6.t6.t30 a5))
% 0.85/1.05 (step t2.t77.t6.t6.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t6.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t34.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t34.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t6.t34.t5))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t6.t34.t6 t2.t77.t6.t6.t34.t8))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t6.t34.t7 t2.t77.t6.t6.t34.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t6.t34.t6 t2.t77.t6.t6.t34.t11))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t6.t34.t10 t2.t77.t6.t6.t34.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t6.t34.t6 t2.t77.t6.t6.t34.t13))
% 0.85/1.05 (step t2.t77.t6.t6.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t34.t14 t2.t77.t6.t6.t34.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t6.t33 t2.t77.t6.t6.t34))
% 0.85/1.05 (step t2.t77.t6.t6.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t6.t37.t5 t2.t77.t6.t6.t37.t6))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t6.t37.t9.t3 t2.t77.t6.t6.t37.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t37.t8 t2.t77.t6.t6.t37.t9))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t6.t37.t7 t2.t77.t6.t6.t37.t10))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t37.t11 t2.t77.t6.t6.t37.t12))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t6.t37.t15.t2 t2.t77.t6.t6.t37.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t37.t14 t2.t77.t6.t6.t37.t15))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t6.t37.t13 t2.t77.t6.t6.t37.t16))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t6.t37.t4 t2.t77.t6.t6.t37.t17))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t6.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t6.t37.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t37.t19 t2.t77.t6.t6.t37.t20))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t6.t37.t18 t2.t77.t6.t6.t37.t21))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t37.t22 t2.t77.t6.t6.t37.t23))
% 0.85/1.05 (step t2.t77.t6.t6.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t6.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t6.t37.t24 t2.t77.t6.t6.t37.t25))
% 0.85/1.05 (step t2.t77.t6.t6.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t6.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t6.t36 t2.t77.t6.t6.t37))
% 0.85/1.05 (step t2.t77.t6.t6.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t6.t35 t2.t77.t6.t6.t38))
% 0.85/1.05 (step t2.t77.t6.t6.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t6.t32 t2.t77.t6.t6.t39 a4))
% 0.85/1.05 (step t2.t77.t6.t6.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t6.t4 t2.t77.t6.t6.t13 t2.t77.t6.t6.t22 t2.t77.t6.t6.t31 t2.t77.t6.t6.t40 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t6.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t6.t41))
% 0.85/1.05 (step t2.t77.t6.t6.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t77.t6.t6.t41))
% 0.85/1.05 (step t2.t77.t6.t6.t44 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t77.t6.t6.t43 t2.t77.t6.t6.t44))
% 0.85/1.05 (step t2.t77.t6.t6.t46 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t77.t6.t6.t45 t2.t77.t6.t6.t46))
% 0.85/1.05 (step t2.t77.t6.t6.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t77.t6.t6.t42 t2.t77.t6.t6.t47))
% 0.85/1.05 (step t2.t77.t6.t6.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t6.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t6.t48 t2.t77.t6.t6.t49))
% 0.85/1.05 (step t2.t77.t6.t6 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t7 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t5 t2.t77.t6.t6))
% 0.85/1.05 (step t2.t77.t6.t8 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t9 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t9.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t77.t6.t9.t5 t2.t77.t6.t9.t6))
% 0.85/1.05 (step t2.t77.t6.t9.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t9.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t9.t7 t2.t77.t6.t9.t8))
% 0.85/1.05 (step t2.t77.t6.t9.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t6.t9.t4 t2.t77.t6.t9.t9))
% 0.85/1.05 (step t2.t77.t6.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t9.t12 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t9.t12.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t9.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t77.t6.t9.t12.t2))
% 0.85/1.05 (step t2.t77.t6.t9.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t9.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t77.t6.t9.t12.t3 t2.t77.t6.t9.t12.t4))
% 0.85/1.05 (step t2.t77.t6.t9.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t9.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t77.t6.t9.t11 t2.t77.t6.t9.t12))
% 0.85/1.05 (step t2.t77.t6.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t77.t6.t9.t10 t2.t77.t6.t9.t13))
% 0.85/1.05 (step t2.t77.t6.t9.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t9.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t9.t14 t2.t77.t6.t9.t15))
% 0.85/1.05 (step t2.t77.t6.t9.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t9.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t9.t16 t2.t77.t6.t9.t17))
% 0.85/1.05 (step t2.t77.t6.t9 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t10 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t8 t2.t77.t6.t9))
% 0.85/1.05 (step t2.t77.t6.t11 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t7 t2.t77.t6.t10))
% 0.85/1.05 (step t2.t77.t6.t12 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t4 t2.t77.t6.t11 a8))
% 0.85/1.05 (step t2.t77.t6.t13 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t14 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t6 t2.t77.t6.t15.t7.t7.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t7 t2.t77.t6.t15.t7.t7.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t6 t2.t77.t6.t15.t7.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t10 t2.t77.t6.t15.t7.t7.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t6 t2.t77.t6.t15.t7.t7.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t7.t14 t2.t77.t6.t15.t7.t7.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t6 t2.t77.t6.t15.t7.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t5 t2.t77.t6.t15.t7.t7.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t9.t3 t2.t77.t6.t15.t7.t7.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t8 t2.t77.t6.t15.t7.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t7 t2.t77.t6.t15.t7.t7.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t11 t2.t77.t6.t15.t7.t7.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t15.t2 t2.t77.t6.t15.t7.t7.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t14 t2.t77.t6.t15.t7.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t13 t2.t77.t6.t15.t7.t7.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t4 t2.t77.t6.t15.t7.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t19 t2.t77.t6.t15.t7.t7.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t18 t2.t77.t6.t15.t7.t7.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t10.t22 t2.t77.t6.t15.t7.t7.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t10.t24 t2.t77.t6.t15.t7.t7.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t9 t2.t77.t6.t15.t7.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t15.t7.t7.t8 t2.t77.t6.t15.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t15.t7.t7.t5 t2.t77.t6.t15.t7.t7.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t7.t7.t4 t2.t77.t6.t15.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t7.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t7.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t16 t2.t77.t6.t15.t7.t7.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t15 t2.t77.t6.t15.t7.t7.t18))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t19 t2.t77.t6.t15.t7.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t7.t21 t2.t77.t6.t15.t7.t7.t22))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t7.t6 t2.t77.t6.t15.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t10.t4 t2.t77.t6.t15.t7.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t7.t10.t8.t3 t2.t77.t6.t15.t7.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t10.t7 t2.t77.t6.t15.t7.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t10.t6 t2.t77.t6.t15.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t7.t10.t10 t2.t77.t6.t15.t7.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t10.t12 t2.t77.t6.t15.t7.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t10.t14 t2.t77.t6.t15.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t15.t7.t10.t16 t2.t77.t6.t15.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t15.t7.t9 t2.t77.t6.t15.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t7.t8 t2.t77.t6.t15.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t15.t7.t5 t2.t77.t6.t15.t7.t12 a5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t7.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t7.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t6 t2.t77.t6.t15.t7.t16.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t7 t2.t77.t6.t15.t7.t16.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t6 t2.t77.t6.t15.t7.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t10 t2.t77.t6.t15.t7.t16.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t6 t2.t77.t6.t15.t7.t16.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t16.t14 t2.t77.t6.t15.t7.t16.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t7.t15 t2.t77.t6.t15.t7.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t5 t2.t77.t6.t15.t7.t19.t6))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t9.t3 t2.t77.t6.t15.t7.t19.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t8 t2.t77.t6.t15.t7.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t7 t2.t77.t6.t15.t7.t19.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t11 t2.t77.t6.t15.t7.t19.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t15.t2 t2.t77.t6.t15.t7.t19.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t14 t2.t77.t6.t15.t7.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t13 t2.t77.t6.t15.t7.t19.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t4 t2.t77.t6.t15.t7.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t19 t2.t77.t6.t15.t7.t19.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t18 t2.t77.t6.t15.t7.t19.t21))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t19.t22 t2.t77.t6.t15.t7.t19.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t7.t19.t24 t2.t77.t6.t15.t7.t19.t25))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t15.t7.t18 t2.t77.t6.t15.t7.t19))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t15.t7.t17 t2.t77.t6.t15.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t15.t7.t14 t2.t77.t6.t15.t7.t21 a4))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t7.t4 t2.t77.t6.t15.t7.t13 t2.t77.t6.t15.t7.t22 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t7.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t7.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t7.t25 t2.t77.t6.t15.t7.t26))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t15.t7.t24 t2.t77.t6.t15.t7.t27))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t6.t15.t7.t28 t2.t77.t6.t15.t7.t29))
% 0.85/1.05 (step t2.t77.t6.t15.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t7.t30 t2.t77.t6.t15.t7.t31))
% 0.85/1.05 (step t2.t77.t6.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t6 t2.t77.t6.t15.t7))
% 0.85/1.05 (step t2.t77.t6.t15.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t10.t4 t2.t77.t6.t15.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t10.t8.t3 t2.t77.t6.t15.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t10.t7 t2.t77.t6.t15.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t10.t6 t2.t77.t6.t15.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t10.t10 t2.t77.t6.t15.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t6.t15.t10.t12 t2.t77.t6.t15.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t10.t14 t2.t77.t6.t15.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t15.t10.t16 t2.t77.t6.t15.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t15.t9 t2.t77.t6.t15.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t8 t2.t77.t6.t15.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t15.t5 t2.t77.t6.t15.t12 a6))
% 0.85/1.05 (step t2.t77.t6.t15.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t16.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t16.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t6 t2.t77.t6.t15.t16.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t7 t2.t77.t6.t15.t16.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t6 t2.t77.t6.t15.t16.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t10 t2.t77.t6.t15.t16.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t6 t2.t77.t6.t15.t16.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t16.t7.t14 t2.t77.t6.t15.t16.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t16.t6 t2.t77.t6.t15.t16.t7))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t5 t2.t77.t6.t15.t16.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t9.t3 t2.t77.t6.t15.t16.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t8 t2.t77.t6.t15.t16.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t7 t2.t77.t6.t15.t16.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t11 t2.t77.t6.t15.t16.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t15.t2 t2.t77.t6.t15.t16.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t14 t2.t77.t6.t15.t16.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t13 t2.t77.t6.t15.t16.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t4 t2.t77.t6.t15.t16.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t19 t2.t77.t6.t15.t16.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t18 t2.t77.t6.t15.t16.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t16.t10.t22 t2.t77.t6.t15.t16.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t16.t10.t24 t2.t77.t6.t15.t16.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t15.t16.t9 t2.t77.t6.t15.t16.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t15.t16.t8 t2.t77.t6.t15.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t15.t16.t5 t2.t77.t6.t15.t16.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t16.t4 t2.t77.t6.t15.t16.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t16.t14))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t16.t14))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t16.t16 t2.t77.t6.t15.t16.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t16.t15 t2.t77.t6.t15.t16.t18))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t15.t16.t19 t2.t77.t6.t15.t16.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t16.t21 t2.t77.t6.t15.t16.t22))
% 0.85/1.05 (step t2.t77.t6.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t15 t2.t77.t6.t15.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t19.t4 t2.t77.t6.t15.t19.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t19.t8.t3 t2.t77.t6.t15.t19.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t19.t7 t2.t77.t6.t15.t19.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t19.t6 t2.t77.t6.t15.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t19.t10 t2.t77.t6.t15.t19.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t19.t12 t2.t77.t6.t15.t19.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t19.t14 t2.t77.t6.t15.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t15.t19.t16 t2.t77.t6.t15.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t15.t18 t2.t77.t6.t15.t19))
% 0.85/1.05 (step t2.t77.t6.t15.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t17 t2.t77.t6.t15.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t15.t14 t2.t77.t6.t15.t21 a5))
% 0.85/1.05 (step t2.t77.t6.t15.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t15.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t25.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t15.t25.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t15.t25.t5))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t15.t25.t6 t2.t77.t6.t15.t25.t8))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t15.t25.t7 t2.t77.t6.t15.t25.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t15.t25.t6 t2.t77.t6.t15.t25.t11))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t15.t25.t10 t2.t77.t6.t15.t25.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t15.t25.t6 t2.t77.t6.t15.t25.t13))
% 0.85/1.05 (step t2.t77.t6.t15.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t25.t14 t2.t77.t6.t15.t25.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t15.t24 t2.t77.t6.t15.t25))
% 0.85/1.05 (step t2.t77.t6.t15.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t15.t28.t5 t2.t77.t6.t15.t28.t6))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t15.t28.t9.t3 t2.t77.t6.t15.t28.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t28.t8 t2.t77.t6.t15.t28.t9))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t15.t28.t7 t2.t77.t6.t15.t28.t10))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t28.t11 t2.t77.t6.t15.t28.t12))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t15.t28.t15.t2 t2.t77.t6.t15.t28.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t28.t14 t2.t77.t6.t15.t28.t15))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t15.t28.t13 t2.t77.t6.t15.t28.t16))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t15.t28.t4 t2.t77.t6.t15.t28.t17))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t15.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t15.t28.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t28.t19 t2.t77.t6.t15.t28.t20))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t15.t28.t18 t2.t77.t6.t15.t28.t21))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t28.t22 t2.t77.t6.t15.t28.t23))
% 0.85/1.05 (step t2.t77.t6.t15.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t15.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t15.t28.t24 t2.t77.t6.t15.t28.t25))
% 0.85/1.05 (step t2.t77.t6.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t15.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t15.t27 t2.t77.t6.t15.t28))
% 0.85/1.05 (step t2.t77.t6.t15.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t15.t26 t2.t77.t6.t15.t29))
% 0.85/1.05 (step t2.t77.t6.t15.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t15.t23 t2.t77.t6.t15.t30 a4))
% 0.85/1.05 (step t2.t77.t6.t15.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t15.t4 t2.t77.t6.t15.t13 t2.t77.t6.t15.t22 t2.t77.t6.t15.t31 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t15.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t77.t6.t15.t32))
% 0.85/1.05 (step t2.t77.t6.t15.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t77.t6.t15.t32))
% 0.85/1.05 (step t2.t77.t6.t15.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t6.t15.t34 t2.t77.t6.t15.t35))
% 0.85/1.05 (step t2.t77.t6.t15.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t77.t6.t15.t36 t2.t77.t6.t15.t37))
% 0.85/1.05 (step t2.t77.t6.t15.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t77.t6.t15.t33 t2.t77.t6.t15.t38))
% 0.85/1.05 (step t2.t77.t6.t15.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t6.t15.t34 t2.t77.t6.t15.t37))
% 0.85/1.05 (step t2.t77.t6.t15.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t77.t6.t15.t40 t2.t77.t6.t15.t35))
% 0.85/1.05 (step t2.t77.t6.t15.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t77.t6.t15.t39 t2.t77.t6.t15.t41))
% 0.85/1.05 (step t2.t77.t6.t15.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t15.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t15.t42 t2.t77.t6.t15.t43))
% 0.85/1.05 (step t2.t77.t6.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t16 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t14 t2.t77.t6.t15))
% 0.85/1.05 (step t2.t77.t6.t17 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t6.t18.t5 t2.t77.t6.t18.t6))
% 0.85/1.05 (step t2.t77.t6.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t77.t6.t18.t7 t2.t77.t6.t18.t8))
% 0.85/1.05 (step t2.t77.t6.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t18.t4 t2.t77.t6.t18.t9))
% 0.85/1.05 (step t2.t77.t6.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t18.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t18.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t18.t12.t3))
% 0.85/1.05 (step t2.t77.t6.t18.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t18.t12.t4 t2.t77.t6.t18.t12.t5))
% 0.85/1.05 (step t2.t77.t6.t18.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t18.t12.t6))
% 0.85/1.05 (step t2.t77.t6.t18.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t18.t11 t2.t77.t6.t18.t12))
% 0.85/1.05 (step t2.t77.t6.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t18.t10 t2.t77.t6.t18.t13))
% 0.85/1.05 (step t2.t77.t6.t18.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t6.t18.t15 t2.t77.t6.t18.t16))
% 0.85/1.05 (step t2.t77.t6.t18.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t77.t6.t18.t17 t2.t77.t6.t18.t18))
% 0.85/1.05 (step t2.t77.t6.t18.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t18.t14 t2.t77.t6.t18.t19))
% 0.85/1.05 (step t2.t77.t6.t18.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t18.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t18.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t18.t22.t3))
% 0.85/1.05 (step t2.t77.t6.t18.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t18.t22.t2 t2.t77.t6.t18.t22.t4))
% 0.85/1.05 (step t2.t77.t6.t18.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t77.t6.t18.t22.t5))
% 0.85/1.05 (step t2.t77.t6.t18.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t18.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t18.t21 t2.t77.t6.t18.t22))
% 0.85/1.05 (step t2.t77.t6.t18.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t18.t20 t2.t77.t6.t18.t23))
% 0.85/1.05 (step t2.t77.t6.t18.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t18.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t18.t24 t2.t77.t6.t18.t25))
% 0.85/1.05 (step t2.t77.t6.t18.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t18.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t77.t6.t18.t26 t2.t77.t6.t18.t27))
% 0.85/1.05 (step t2.t77.t6.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t19 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t6.t17 t2.t77.t6.t18))
% 0.85/1.05 (step t2.t77.t6.t20 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t77.t6.t16 t2.t77.t6.t19))
% 0.85/1.05 (step t2.t77.t6.t21 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t77.t6.t13 t2.t77.t6.t20 a7))
% 0.85/1.05 (step t2.t77.t6.t22 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t23 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t24.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t24.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t24.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t24.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t24.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t6 t2.t77.t6.t24.t7.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t7 t2.t77.t6.t24.t7.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t6 t2.t77.t6.t24.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t10 t2.t77.t6.t24.t7.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t6 t2.t77.t6.t24.t7.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t7.t7.t14 t2.t77.t6.t24.t7.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t24.t7.t6 t2.t77.t6.t24.t7.t7))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t5 t2.t77.t6.t24.t7.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t9.t3 t2.t77.t6.t24.t7.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t8 t2.t77.t6.t24.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t7 t2.t77.t6.t24.t7.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t11 t2.t77.t6.t24.t7.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t15.t2 t2.t77.t6.t24.t7.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t14 t2.t77.t6.t24.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t13 t2.t77.t6.t24.t7.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t4 t2.t77.t6.t24.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t19 t2.t77.t6.t24.t7.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t18 t2.t77.t6.t24.t7.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t7.t10.t22 t2.t77.t6.t24.t7.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t24.t7.t10.t24 t2.t77.t6.t24.t7.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t24.t7.t9 t2.t77.t6.t24.t7.t10))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t24.t7.t8 t2.t77.t6.t24.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t24.t7.t5 t2.t77.t6.t24.t7.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t24.t7.t4 t2.t77.t6.t24.t7.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t24.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t24.t7.t14))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t24.t7.t16 t2.t77.t6.t24.t7.t17))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t24.t7.t15 t2.t77.t6.t24.t7.t18))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t24.t7.t19 t2.t77.t6.t24.t7.t20))
% 0.85/1.05 (step t2.t77.t6.t24.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t7.t21 t2.t77.t6.t24.t7.t22))
% 0.85/1.05 (step t2.t77.t6.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t24.t6 t2.t77.t6.t24.t7))
% 0.85/1.05 (step t2.t77.t6.t24.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t24.t10.t4 t2.t77.t6.t24.t10.t5))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t24.t10.t8.t3 t2.t77.t6.t24.t10.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t10.t7 t2.t77.t6.t24.t10.t8))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t10.t6 t2.t77.t6.t24.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t24.t10.t10 t2.t77.t6.t24.t10.t11))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t10.t12 t2.t77.t6.t24.t10.t13))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t10.t14 t2.t77.t6.t24.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t24.t10.t16 t2.t77.t6.t24.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t24.t9 t2.t77.t6.t24.t10))
% 0.85/1.05 (step t2.t77.t6.t24.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t24.t8 t2.t77.t6.t24.t11))
% 0.85/1.05 (step t2.t77.t6.t24.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t24.t5 t2.t77.t6.t24.t12 a5))
% 0.85/1.05 (step t2.t77.t6.t24.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t24.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t24.t16.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t24.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t24.t16.t5))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t24.t16.t6 t2.t77.t6.t24.t16.t8))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t24.t16.t7 t2.t77.t6.t24.t16.t9))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t24.t16.t6 t2.t77.t6.t24.t16.t11))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t24.t16.t10 t2.t77.t6.t24.t16.t12))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t24.t16.t6 t2.t77.t6.t24.t16.t13))
% 0.85/1.05 (step t2.t77.t6.t24.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t16.t14 t2.t77.t6.t24.t16.t15))
% 0.85/1.05 (step t2.t77.t6.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t24.t15 t2.t77.t6.t24.t16))
% 0.85/1.05 (step t2.t77.t6.t24.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t24.t19.t5 t2.t77.t6.t24.t19.t6))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t24.t19.t9.t3 t2.t77.t6.t24.t19.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t19.t8 t2.t77.t6.t24.t19.t9))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t24.t19.t7 t2.t77.t6.t24.t19.t10))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t24.t19.t11 t2.t77.t6.t24.t19.t12))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t24.t19.t15.t2 t2.t77.t6.t24.t19.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t24.t19.t14 t2.t77.t6.t24.t19.t15))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t24.t19.t13 t2.t77.t6.t24.t19.t16))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t24.t19.t4 t2.t77.t6.t24.t19.t17))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t24.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t24.t19.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t24.t19.t19 t2.t77.t6.t24.t19.t20))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t24.t19.t18 t2.t77.t6.t24.t19.t21))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t19.t22 t2.t77.t6.t24.t19.t23))
% 0.85/1.05 (step t2.t77.t6.t24.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t24.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t24.t19.t24 t2.t77.t6.t24.t19.t25))
% 0.85/1.05 (step t2.t77.t6.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t24.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t24.t18 t2.t77.t6.t24.t19))
% 0.85/1.05 (step t2.t77.t6.t24.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t24.t17 t2.t77.t6.t24.t20))
% 0.85/1.05 (step t2.t77.t6.t24.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t24.t14 t2.t77.t6.t24.t21 a4))
% 0.85/1.05 (step t2.t77.t6.t24.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t24.t4 t2.t77.t6.t24.t13 t2.t77.t6.t24.t22 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t24.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t24.t23))
% 0.85/1.05 (step t2.t77.t6.t24.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t24.t23))
% 0.85/1.05 (step t2.t77.t6.t24.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t24.t25 t2.t77.t6.t24.t26))
% 0.85/1.05 (step t2.t77.t6.t24.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t24.t24 t2.t77.t6.t24.t27))
% 0.85/1.05 (step t2.t77.t6.t24.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t6.t24.t28 t2.t77.t6.t24.t29))
% 0.85/1.05 (step t2.t77.t6.t24.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t24.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t24.t30 t2.t77.t6.t24.t31))
% 0.85/1.05 (step t2.t77.t6.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t25 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t23 t2.t77.t6.t24))
% 0.85/1.05 (step t2.t77.t6.t26 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t27.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t27.t4 t2.t77.t6.t27.t5))
% 0.85/1.05 (step t2.t77.t6.t27.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t27.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t27.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t27.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t27.t8.t3 t2.t77.t6.t27.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t27.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t27.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t27.t7 t2.t77.t6.t27.t8))
% 0.85/1.05 (step t2.t77.t6.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t27.t6 t2.t77.t6.t27.t9))
% 0.85/1.05 (step t2.t77.t6.t27.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t6.t27.t10 t2.t77.t6.t27.t11))
% 0.85/1.05 (step t2.t77.t6.t27.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t27.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t6.t27.t12 t2.t77.t6.t27.t13))
% 0.85/1.05 (step t2.t77.t6.t27.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t27.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t27.t14 t2.t77.t6.t27.t15))
% 0.85/1.05 (step t2.t77.t6.t27.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t27.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t27.t16 t2.t77.t6.t27.t17))
% 0.85/1.05 (step t2.t77.t6.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t28 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t26 t2.t77.t6.t27))
% 0.85/1.05 (step t2.t77.t6.t29 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t25 t2.t77.t6.t28))
% 0.85/1.05 (step t2.t77.t6.t30 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t22 t2.t77.t6.t29 a6))
% 0.85/1.05 (step t2.t77.t6.t31 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t32 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t33.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t33.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t33.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t33.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t33.t7.t5))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t33.t7.t6 t2.t77.t6.t33.t7.t8))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t33.t7.t7 t2.t77.t6.t33.t7.t9))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t33.t7.t6 t2.t77.t6.t33.t7.t11))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t33.t7.t10 t2.t77.t6.t33.t7.t12))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t33.t7.t6 t2.t77.t6.t33.t7.t13))
% 0.85/1.05 (step t2.t77.t6.t33.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t33.t7.t14 t2.t77.t6.t33.t7.t15))
% 0.85/1.05 (step t2.t77.t6.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t33.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t33.t6 t2.t77.t6.t33.t7))
% 0.85/1.05 (step t2.t77.t6.t33.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t33.t10.t5 t2.t77.t6.t33.t10.t6))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t33.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t33.t10.t9.t3 t2.t77.t6.t33.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t33.t10.t8 t2.t77.t6.t33.t10.t9))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t33.t10.t7 t2.t77.t6.t33.t10.t10))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t33.t10.t11 t2.t77.t6.t33.t10.t12))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t33.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t33.t10.t15.t2 t2.t77.t6.t33.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t33.t10.t14 t2.t77.t6.t33.t10.t15))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t33.t10.t13 t2.t77.t6.t33.t10.t16))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t33.t10.t4 t2.t77.t6.t33.t10.t17))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t33.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t33.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t33.t10.t19 t2.t77.t6.t33.t10.t20))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t33.t10.t18 t2.t77.t6.t33.t10.t21))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t33.t10.t22 t2.t77.t6.t33.t10.t23))
% 0.85/1.05 (step t2.t77.t6.t33.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t33.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t33.t10.t24 t2.t77.t6.t33.t10.t25))
% 0.85/1.05 (step t2.t77.t6.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t33.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t33.t9 t2.t77.t6.t33.t10))
% 0.85/1.05 (step t2.t77.t6.t33.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t33.t8 t2.t77.t6.t33.t11))
% 0.85/1.05 (step t2.t77.t6.t33.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t33.t5 t2.t77.t6.t33.t12 a4))
% 0.85/1.05 (step t2.t77.t6.t33.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t33.t4 t2.t77.t6.t33.t13 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t33.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t33.t14))
% 0.85/1.05 (step t2.t77.t6.t33.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t33.t14))
% 0.85/1.05 (step t2.t77.t6.t33.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t33.t16 t2.t77.t6.t33.t17))
% 0.85/1.05 (step t2.t77.t6.t33.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t33.t15 t2.t77.t6.t33.t18))
% 0.85/1.05 (step t2.t77.t6.t33.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t6.t33.t19 t2.t77.t6.t33.t20))
% 0.85/1.05 (step t2.t77.t6.t33.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t33.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t33.t21 t2.t77.t6.t33.t22))
% 0.85/1.05 (step t2.t77.t6.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t34 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t32 t2.t77.t6.t33))
% 0.85/1.05 (step t2.t77.t6.t35 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t36.t4 t2.t77.t6.t36.t5))
% 0.85/1.05 (step t2.t77.t6.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t36.t8.t3 t2.t77.t6.t36.t8.t4))
% 0.85/1.05 (step t2.t77.t6.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t36.t7 t2.t77.t6.t36.t8))
% 0.85/1.05 (step t2.t77.t6.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t36.t6 t2.t77.t6.t36.t9))
% 0.85/1.05 (step t2.t77.t6.t36.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t6.t36.t10 t2.t77.t6.t36.t11))
% 0.85/1.05 (step t2.t77.t6.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t36.t12 t2.t77.t6.t36.t13))
% 0.85/1.05 (step t2.t77.t6.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t36.t14 t2.t77.t6.t36.t15))
% 0.85/1.05 (step t2.t77.t6.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t6.t36.t16 t2.t77.t6.t36.t17))
% 0.85/1.05 (step t2.t77.t6.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t37 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t35 t2.t77.t6.t36))
% 0.85/1.05 (step t2.t77.t6.t38 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t34 t2.t77.t6.t37))
% 0.85/1.05 (step t2.t77.t6.t39 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t6.t31 t2.t77.t6.t38 a5))
% 0.85/1.05 (step t2.t77.t6.t40 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t6.t41 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t6.t42.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t42.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t42.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t42.t5))
% 0.85/1.05 (step t2.t77.t6.t42.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t6.t42.t5))
% 0.85/1.05 (step t2.t77.t6.t42.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t6.t42.t6 t2.t77.t6.t42.t8))
% 0.85/1.05 (step t2.t77.t6.t42.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t6.t42.t7 t2.t77.t6.t42.t9))
% 0.85/1.05 (step t2.t77.t6.t42.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t6.t42.t6 t2.t77.t6.t42.t11))
% 0.85/1.05 (step t2.t77.t6.t42.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t6.t42.t10 t2.t77.t6.t42.t12))
% 0.85/1.05 (step t2.t77.t6.t42.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t6.t42.t6 t2.t77.t6.t42.t13))
% 0.85/1.05 (step t2.t77.t6.t42.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t42.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t42.t14 t2.t77.t6.t42.t15))
% 0.85/1.05 (step t2.t77.t6.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t43 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t41 t2.t77.t6.t42))
% 0.85/1.05 (step t2.t77.t6.t44 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t6.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t6.t45.t5 t2.t77.t6.t45.t6))
% 0.85/1.05 (step t2.t77.t6.t45.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t45.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t45.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t6.t45.t9.t3 t2.t77.t6.t45.t9.t4))
% 0.85/1.05 (step t2.t77.t6.t45.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t45.t8 t2.t77.t6.t45.t9))
% 0.85/1.05 (step t2.t77.t6.t45.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t6.t45.t7 t2.t77.t6.t45.t10))
% 0.85/1.05 (step t2.t77.t6.t45.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t45.t11 t2.t77.t6.t45.t12))
% 0.85/1.05 (step t2.t77.t6.t45.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t45.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t45.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t6.t45.t15.t2 t2.t77.t6.t45.t15.t3))
% 0.85/1.05 (step t2.t77.t6.t45.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t45.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t45.t14 t2.t77.t6.t45.t15))
% 0.85/1.05 (step t2.t77.t6.t45.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t6.t45.t13 t2.t77.t6.t45.t16))
% 0.85/1.05 (step t2.t77.t6.t45.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t6.t45.t4 t2.t77.t6.t45.t17))
% 0.85/1.05 (step t2.t77.t6.t45.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t6.t45.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t6.t45.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t6.t45.t20.t2))
% 0.85/1.05 (step t2.t77.t6.t45.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t45.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t45.t19 t2.t77.t6.t45.t20))
% 0.85/1.05 (step t2.t77.t6.t45.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t6.t45.t18 t2.t77.t6.t45.t21))
% 0.85/1.05 (step t2.t77.t6.t45.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t45.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t45.t22 t2.t77.t6.t45.t23))
% 0.85/1.05 (step t2.t77.t6.t45.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t6.t45.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t6.t45.t24 t2.t77.t6.t45.t25))
% 0.85/1.05 (step t2.t77.t6.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t46 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t6.t44 t2.t77.t6.t45))
% 0.85/1.05 (step t2.t77.t6.t47 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t6.t43 t2.t77.t6.t46))
% 0.85/1.05 (step t2.t77.t6.t48 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t6.t40 t2.t77.t6.t47 a4))
% 0.85/1.05 (step t2.t77.t6.t49 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t6.t3 a10 a9 t2.t77.t6.t12 t2.t77.t6.t21 t2.t77.t6.t30 t2.t77.t6.t39 t2.t77.t6.t48 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t6.t50 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t6.t49))
% 0.85/1.05 (step t2.t77.t6.t51 (cl (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule and :premises (t2.t77.t6.t49))
% 0.85/1.05 (anchor :step t2.t77.t6.t52 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t6.t52.t1 (cl (= X X)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t52.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t52.t3 (cl (= (@ Phi X) (@ Phi X))) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t52.t4 (cl (= (@ tptp.mnot (@ Phi X)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)))) :rule cong :premises (t2.t77.t6.t50 t2.t77.t6.t52.t3))
% 0.85/1.05 (step t2.t77.t6.t52.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t52.t6 (cl (= (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t52.t4 t2.t77.t6.t52.t5))
% 0.85/1.05 (step t2.t77.t6.t52 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t6.t53 (cl (= (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))))) :rule cong :premises (t2.t77.t6.t51 t2.t77.t6.t52))
% 0.85/1.05 (step t2.t77.t6.t54 (cl (= (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))))) :rule cong :premises (t2.t77.t6.t50 t2.t77.t6.t53))
% 0.85/1.05 (step t2.t77.t6.t55 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t6.t56 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t77.t6.t54 t2.t77.t6.t55))
% 0.85/1.05 (step t2.t77.t6 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t7 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t77.t5 t2.t77.t6))
% 0.85/1.05 (step t2.t77.t8 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t9 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t4 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t9.t5 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t9.t5.t1 (cl (= X X)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0))) :rule cong :premises (t2.t77.t9.t5.t3 t2.t77.t9.t5.t4))
% 0.85/1.05 (step t2.t77.t9.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule trans :premises (t2.t77.t9.t5.t5 t2.t77.t9.t5.t6))
% 0.85/1.05 (step t2.t77.t9.t5 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule bind)
% 0.85/1.05 (step t2.t77.t9.t6 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule cong :premises (t2.t77.t9.t4 t2.t77.t9.t5))
% 0.85/1.05 (step t2.t77.t9.t7 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t9.t8 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t9.t8.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t9.t8.t2 :args ((X tptp.mu) (:= X X)))
% 0.85/1.05 (step t2.t77.t9.t8.t2.t1 (cl (= X X)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t8.t2.t2 (cl (= (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t8.t2.t4 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W))) :rule cong :premises (t2.t77.t9.t8.t2.t2 t2.t77.t9.t8.t2.t3))
% 0.85/1.05 (step t2.t77.t9.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W) (not (@ (@ Phi X) W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t8.t2.t6 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (not (@ (@ Phi X) W)))) :rule trans :premises (t2.t77.t9.t8.t2.t4 t2.t77.t9.t8.t2.t5))
% 0.85/1.05 (step t2.t77.t9.t8.t2 (cl (= (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t9.t8 (cl (= (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t9.t9 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t77.t9.t7 t2.t77.t9.t8))
% 0.85/1.05 (step t2.t77.t9.t10 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t77.t9.t6 t2.t77.t9.t9))
% 0.85/1.05 (step t2.t77.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule cong :premises (t2.t77.t9.t3 t2.t77.t9.t10))
% 0.85/1.05 (step t2.t77.t9.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t9.t13 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t9.t13.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule cong :premises (t2.t77.t9.t13.t2))
% 0.85/1.05 (step t2.t77.t9.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t77.t9.t12 t2.t77.t9.t13))
% 0.85/1.05 (step t2.t77.t9.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t77.t9.t11 t2.t77.t9.t14))
% 0.85/1.05 (step t2.t77.t9.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t9.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t9.t15 t2.t77.t9.t16))
% 0.85/1.05 (step t2.t77.t9.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t9.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule trans :premises (t2.t77.t9.t17 t2.t77.t9.t18))
% 0.85/1.05 (step t2.t77.t9 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t10 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule cong :premises (t2.t77.t8 t2.t77.t9))
% 0.85/1.05 (step t2.t77.t11 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule trans :premises (t2.t77.t7 t2.t77.t10))
% 0.85/1.05 (step t2.t77.t12 (cl (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule resolution :premises (t2.t77.t4 t2.t77.t11 a11))
% 0.85/1.05 (step t2.t77.t13 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t14 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t15.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t15.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t15.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t15.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t7.t7.t7.t5))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t6 t2.t77.t15.t7.t7.t7.t7.t8))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t7 t2.t77.t15.t7.t7.t7.t7.t9))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t6 t2.t77.t15.t7.t7.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t10 t2.t77.t15.t7.t7.t7.t7.t12))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t6 t2.t77.t15.t7.t7.t7.t7.t13))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t7.t14 t2.t77.t15.t7.t7.t7.t7.t15))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t6 t2.t77.t15.t7.t7.t7.t7))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t5 t2.t77.t15.t7.t7.t7.t10.t6))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t9.t3 t2.t77.t15.t7.t7.t7.t10.t9.t4))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t8 t2.t77.t15.t7.t7.t7.t10.t9))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t7 t2.t77.t15.t7.t7.t7.t10.t10))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t11 t2.t77.t15.t7.t7.t7.t10.t12))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t15.t2 t2.t77.t15.t7.t7.t7.t10.t15.t3))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t14 t2.t77.t15.t7.t7.t7.t10.t15))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t13 t2.t77.t15.t7.t7.t7.t10.t16))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t4 t2.t77.t15.t7.t7.t7.t10.t17))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.05 (anchor :step t2.t77.t15.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t20.t2))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t19 t2.t77.t15.t7.t7.t7.t10.t20))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t18 t2.t77.t15.t7.t7.t7.t10.t21))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t10.t22 t2.t77.t15.t7.t7.t7.t10.t23))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t10.t24 t2.t77.t15.t7.t7.t7.t10.t25))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t9 t2.t77.t15.t7.t7.t7.t10))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t7.t7.t7.t8 t2.t77.t15.t7.t7.t7.t11))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t7.t7.t7.t5 t2.t77.t15.t7.t7.t7.t12 a4))
% 0.85/1.05 (step t2.t77.t15.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t7.t7.t4 t2.t77.t15.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t7.t7.t14))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t7.t7.t14))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t16 t2.t77.t15.t7.t7.t7.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t15 t2.t77.t15.t7.t7.t7.t18))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t19 t2.t77.t15.t7.t7.t7.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t7.t21 t2.t77.t15.t7.t7.t7.t22))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t7.t6 t2.t77.t15.t7.t7.t7))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t10.t4 t2.t77.t15.t7.t7.t10.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t7.t10.t8.t3 t2.t77.t15.t7.t7.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t10.t7 t2.t77.t15.t7.t7.t10.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t10.t6 t2.t77.t15.t7.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t7.t10.t10 t2.t77.t15.t7.t7.t10.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t10.t12 t2.t77.t15.t7.t7.t10.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t10.t14 t2.t77.t15.t7.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t7.t7.t10.t16 t2.t77.t15.t7.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t7.t7.t9 t2.t77.t15.t7.t7.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t7.t8 t2.t77.t15.t7.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t7.t7.t5 t2.t77.t15.t7.t7.t12 a5))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t7.t16.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t7.t16.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t6 t2.t77.t15.t7.t7.t16.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t7 t2.t77.t15.t7.t7.t16.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t6 t2.t77.t15.t7.t7.t16.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t10 t2.t77.t15.t7.t7.t16.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t6 t2.t77.t15.t7.t7.t16.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t16.t14 t2.t77.t15.t7.t7.t16.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t7.t15 t2.t77.t15.t7.t7.t16))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t5 t2.t77.t15.t7.t7.t19.t6))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t9.t3 t2.t77.t15.t7.t7.t19.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t8 t2.t77.t15.t7.t7.t19.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t7 t2.t77.t15.t7.t7.t19.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t11 t2.t77.t15.t7.t7.t19.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t15.t2 t2.t77.t15.t7.t7.t19.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t14 t2.t77.t15.t7.t7.t19.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t13 t2.t77.t15.t7.t7.t19.t16))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t4 t2.t77.t15.t7.t7.t19.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t19 t2.t77.t15.t7.t7.t19.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t18 t2.t77.t15.t7.t7.t19.t21))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t19.t22 t2.t77.t15.t7.t7.t19.t23))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t7.t19.t24 t2.t77.t15.t7.t7.t19.t25))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t7.t7.t18 t2.t77.t15.t7.t7.t19))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t7.t7.t17 t2.t77.t15.t7.t7.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t7.t7.t14 t2.t77.t15.t7.t7.t21 a4))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t7.t4 t2.t77.t15.t7.t7.t13 t2.t77.t15.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t7.t23))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t7.t23))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t7.t25 t2.t77.t15.t7.t7.t26))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t7.t7.t24 t2.t77.t15.t7.t7.t27))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t15.t7.t7.t28 t2.t77.t15.t7.t7.t29))
% 0.85/1.06 (step t2.t77.t15.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t7.t30 t2.t77.t15.t7.t7.t31))
% 0.85/1.06 (step t2.t77.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t6 t2.t77.t15.t7.t7))
% 0.85/1.06 (step t2.t77.t15.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t10.t4 t2.t77.t15.t7.t10.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t10.t8.t3 t2.t77.t15.t7.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t10.t7 t2.t77.t15.t7.t10.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t10.t6 t2.t77.t15.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t10.t10 t2.t77.t15.t7.t10.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t15.t7.t10.t12 t2.t77.t15.t7.t10.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t10.t14 t2.t77.t15.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t7.t10.t16 t2.t77.t15.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t7.t9 t2.t77.t15.t7.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t8 t2.t77.t15.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t7.t5 t2.t77.t15.t7.t12 a6))
% 0.85/1.06 (step t2.t77.t15.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t16.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t16.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t6 t2.t77.t15.t7.t16.t7.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t7 t2.t77.t15.t7.t16.t7.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t6 t2.t77.t15.t7.t16.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t10 t2.t77.t15.t7.t16.t7.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t6 t2.t77.t15.t7.t16.t7.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t16.t7.t14 t2.t77.t15.t7.t16.t7.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t16.t6 t2.t77.t15.t7.t16.t7))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t5 t2.t77.t15.t7.t16.t10.t6))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t9.t3 t2.t77.t15.t7.t16.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t8 t2.t77.t15.t7.t16.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t7 t2.t77.t15.t7.t16.t10.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t11 t2.t77.t15.t7.t16.t10.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t15.t2 t2.t77.t15.t7.t16.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t14 t2.t77.t15.t7.t16.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t13 t2.t77.t15.t7.t16.t10.t16))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t4 t2.t77.t15.t7.t16.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t19 t2.t77.t15.t7.t16.t10.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t18 t2.t77.t15.t7.t16.t10.t21))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t16.t10.t22 t2.t77.t15.t7.t16.t10.t23))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t16.t10.t24 t2.t77.t15.t7.t16.t10.t25))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t7.t16.t9 t2.t77.t15.t7.t16.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t7.t16.t8 t2.t77.t15.t7.t16.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t7.t16.t5 t2.t77.t15.t7.t16.t12 a4))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t16.t4 t2.t77.t15.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t16.t14))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t16.t14))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t16.t16 t2.t77.t15.t7.t16.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t16.t15 t2.t77.t15.t7.t16.t18))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t15.t7.t16.t19 t2.t77.t15.t7.t16.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t16.t21 t2.t77.t15.t7.t16.t22))
% 0.85/1.06 (step t2.t77.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t15 t2.t77.t15.t7.t16))
% 0.85/1.06 (step t2.t77.t15.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t19.t4 t2.t77.t15.t7.t19.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t19.t8.t3 t2.t77.t15.t7.t19.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t19.t7 t2.t77.t15.t7.t19.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t19.t6 t2.t77.t15.t7.t19.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t19.t10 t2.t77.t15.t7.t19.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t19.t12 t2.t77.t15.t7.t19.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t19.t14 t2.t77.t15.t7.t19.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t7.t19.t16 t2.t77.t15.t7.t19.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t7.t18 t2.t77.t15.t7.t19))
% 0.85/1.06 (step t2.t77.t15.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t17 t2.t77.t15.t7.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t7.t14 t2.t77.t15.t7.t21 a5))
% 0.85/1.06 (step t2.t77.t15.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t7.t25.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t7.t25.t5))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t7.t25.t6 t2.t77.t15.t7.t25.t8))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t7.t25.t7 t2.t77.t15.t7.t25.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t7.t25.t6 t2.t77.t15.t7.t25.t11))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t7.t25.t10 t2.t77.t15.t7.t25.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t7.t25.t6 t2.t77.t15.t7.t25.t13))
% 0.85/1.06 (step t2.t77.t15.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t25.t14 t2.t77.t15.t7.t25.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t7.t24 t2.t77.t15.t7.t25))
% 0.85/1.06 (step t2.t77.t15.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t7.t28.t5 t2.t77.t15.t7.t28.t6))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t7.t28.t9.t3 t2.t77.t15.t7.t28.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t28.t8 t2.t77.t15.t7.t28.t9))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t7.t28.t7 t2.t77.t15.t7.t28.t10))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t28.t11 t2.t77.t15.t7.t28.t12))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t7.t28.t15.t2 t2.t77.t15.t7.t28.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t28.t14 t2.t77.t15.t7.t28.t15))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t7.t28.t13 t2.t77.t15.t7.t28.t16))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t7.t28.t4 t2.t77.t15.t7.t28.t17))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t7.t28.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t28.t19 t2.t77.t15.t7.t28.t20))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t7.t28.t18 t2.t77.t15.t7.t28.t21))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t28.t22 t2.t77.t15.t7.t28.t23))
% 0.85/1.06 (step t2.t77.t15.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t7.t28.t24 t2.t77.t15.t7.t28.t25))
% 0.85/1.06 (step t2.t77.t15.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t7.t27 t2.t77.t15.t7.t28))
% 0.85/1.06 (step t2.t77.t15.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t7.t26 t2.t77.t15.t7.t29))
% 0.85/1.06 (step t2.t77.t15.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t7.t23 t2.t77.t15.t7.t30 a4))
% 0.85/1.06 (step t2.t77.t15.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t7.t4 t2.t77.t15.t7.t13 t2.t77.t15.t7.t22 t2.t77.t15.t7.t31 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t77.t15.t7.t32))
% 0.85/1.06 (step t2.t77.t15.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t77.t15.t7.t32))
% 0.85/1.06 (step t2.t77.t15.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t15.t7.t34 t2.t77.t15.t7.t35))
% 0.85/1.06 (step t2.t77.t15.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t77.t15.t7.t36 t2.t77.t15.t7.t37))
% 0.85/1.06 (step t2.t77.t15.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t77.t15.t7.t33 t2.t77.t15.t7.t38))
% 0.85/1.06 (step t2.t77.t15.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t15.t7.t34 t2.t77.t15.t7.t37))
% 0.85/1.06 (step t2.t77.t15.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t77.t15.t7.t40 t2.t77.t15.t7.t35))
% 0.85/1.06 (step t2.t77.t15.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t77.t15.t7.t39 t2.t77.t15.t7.t41))
% 0.85/1.06 (step t2.t77.t15.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t7.t42 t2.t77.t15.t7.t43))
% 0.85/1.06 (step t2.t77.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t6 t2.t77.t15.t7))
% 0.85/1.06 (step t2.t77.t15.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t15.t10.t5 t2.t77.t15.t10.t6))
% 0.85/1.06 (step t2.t77.t15.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t77.t15.t10.t7 t2.t77.t15.t10.t8))
% 0.85/1.06 (step t2.t77.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t10.t4 t2.t77.t15.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t10.t12.t3))
% 0.85/1.06 (step t2.t77.t15.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t10.t12.t4 t2.t77.t15.t10.t12.t5))
% 0.85/1.06 (step t2.t77.t15.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t10.t12.t6))
% 0.85/1.06 (step t2.t77.t15.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t15.t10.t11 t2.t77.t15.t10.t12))
% 0.85/1.06 (step t2.t77.t15.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t15.t10.t10 t2.t77.t15.t10.t13))
% 0.85/1.06 (step t2.t77.t15.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t15.t10.t15 t2.t77.t15.t10.t16))
% 0.85/1.06 (step t2.t77.t15.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t77.t15.t10.t17 t2.t77.t15.t10.t18))
% 0.85/1.06 (step t2.t77.t15.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t10.t14 t2.t77.t15.t10.t19))
% 0.85/1.06 (step t2.t77.t15.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t10.t22.t3))
% 0.85/1.06 (step t2.t77.t15.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t10.t22.t2 t2.t77.t15.t10.t22.t4))
% 0.85/1.06 (step t2.t77.t15.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t77.t15.t10.t22.t5))
% 0.85/1.06 (step t2.t77.t15.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t10.t21 t2.t77.t15.t10.t22))
% 0.85/1.06 (step t2.t77.t15.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t10.t20 t2.t77.t15.t10.t23))
% 0.85/1.06 (step t2.t77.t15.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t10.t24 t2.t77.t15.t10.t25))
% 0.85/1.06 (step t2.t77.t15.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t77.t15.t10.t26 t2.t77.t15.t10.t27))
% 0.85/1.06 (step t2.t77.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t15.t9 t2.t77.t15.t10))
% 0.85/1.06 (step t2.t77.t15.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t77.t15.t8 t2.t77.t15.t11))
% 0.85/1.06 (step t2.t77.t15.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t77.t15.t5 t2.t77.t15.t12 a7))
% 0.85/1.06 (step t2.t77.t15.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t16.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t16.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t6 t2.t77.t15.t16.t7.t7.t8))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t7 t2.t77.t15.t16.t7.t7.t9))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t6 t2.t77.t15.t16.t7.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t10 t2.t77.t15.t16.t7.t7.t12))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t6 t2.t77.t15.t16.t7.t7.t13))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t7.t7.t14 t2.t77.t15.t16.t7.t7.t15))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t16.t7.t6 t2.t77.t15.t16.t7.t7))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t5 t2.t77.t15.t16.t7.t10.t6))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t9.t3 t2.t77.t15.t16.t7.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t8 t2.t77.t15.t16.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t7 t2.t77.t15.t16.t7.t10.t10))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t11 t2.t77.t15.t16.t7.t10.t12))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t15.t2 t2.t77.t15.t16.t7.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t14 t2.t77.t15.t16.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t13 t2.t77.t15.t16.t7.t10.t16))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t4 t2.t77.t15.t16.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t19 t2.t77.t15.t16.t7.t10.t20))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t18 t2.t77.t15.t16.t7.t10.t21))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t7.t10.t22 t2.t77.t15.t16.t7.t10.t23))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t16.t7.t10.t24 t2.t77.t15.t16.t7.t10.t25))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t16.t7.t9 t2.t77.t15.t16.t7.t10))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t16.t7.t8 t2.t77.t15.t16.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t16.t7.t5 t2.t77.t15.t16.t7.t12 a4))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t16.t7.t4 t2.t77.t15.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t16.t7.t14))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t16.t7.t14))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t16.t7.t16 t2.t77.t15.t16.t7.t17))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t16.t7.t15 t2.t77.t15.t16.t7.t18))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t15.t16.t7.t19 t2.t77.t15.t16.t7.t20))
% 0.85/1.06 (step t2.t77.t15.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t7.t21 t2.t77.t15.t16.t7.t22))
% 0.85/1.06 (step t2.t77.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t16.t6 t2.t77.t15.t16.t7))
% 0.85/1.06 (step t2.t77.t15.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t16.t10.t4 t2.t77.t15.t16.t10.t5))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t16.t10.t8.t3 t2.t77.t15.t16.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t10.t7 t2.t77.t15.t16.t10.t8))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t10.t6 t2.t77.t15.t16.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t15.t16.t10.t10 t2.t77.t15.t16.t10.t11))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t10.t12 t2.t77.t15.t16.t10.t13))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t10.t14 t2.t77.t15.t16.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t16.t10.t16 t2.t77.t15.t16.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t16.t9 t2.t77.t15.t16.t10))
% 0.85/1.06 (step t2.t77.t15.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t16.t8 t2.t77.t15.t16.t11))
% 0.85/1.06 (step t2.t77.t15.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t16.t5 t2.t77.t15.t16.t12 a5))
% 0.85/1.06 (step t2.t77.t15.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t16.t16.t5))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t16.t16.t5))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t16.t16.t6 t2.t77.t15.t16.t16.t8))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t16.t16.t7 t2.t77.t15.t16.t16.t9))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t16.t16.t6 t2.t77.t15.t16.t16.t11))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t16.t16.t10 t2.t77.t15.t16.t16.t12))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t16.t16.t6 t2.t77.t15.t16.t16.t13))
% 0.85/1.06 (step t2.t77.t15.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t16.t14 t2.t77.t15.t16.t16.t15))
% 0.85/1.06 (step t2.t77.t15.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t16.t15 t2.t77.t15.t16.t16))
% 0.85/1.06 (step t2.t77.t15.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t16.t19.t5 t2.t77.t15.t16.t19.t6))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t16.t19.t9.t3 t2.t77.t15.t16.t19.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t19.t8 t2.t77.t15.t16.t19.t9))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t16.t19.t7 t2.t77.t15.t16.t19.t10))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t16.t19.t11 t2.t77.t15.t16.t19.t12))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t16.t19.t15.t2 t2.t77.t15.t16.t19.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t16.t19.t14 t2.t77.t15.t16.t19.t15))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t16.t19.t13 t2.t77.t15.t16.t19.t16))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t16.t19.t4 t2.t77.t15.t16.t19.t17))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t16.t19.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t16.t19.t19 t2.t77.t15.t16.t19.t20))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t16.t19.t18 t2.t77.t15.t16.t19.t21))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t19.t22 t2.t77.t15.t16.t19.t23))
% 0.85/1.06 (step t2.t77.t15.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t16.t19.t24 t2.t77.t15.t16.t19.t25))
% 0.85/1.06 (step t2.t77.t15.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t16.t18 t2.t77.t15.t16.t19))
% 0.85/1.06 (step t2.t77.t15.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t16.t17 t2.t77.t15.t16.t20))
% 0.85/1.06 (step t2.t77.t15.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t16.t14 t2.t77.t15.t16.t21 a4))
% 0.85/1.06 (step t2.t77.t15.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t16.t4 t2.t77.t15.t16.t13 t2.t77.t15.t16.t22 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t16.t23))
% 0.85/1.06 (step t2.t77.t15.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t16.t23))
% 0.85/1.06 (step t2.t77.t15.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t16.t25 t2.t77.t15.t16.t26))
% 0.85/1.06 (step t2.t77.t15.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t16.t24 t2.t77.t15.t16.t27))
% 0.85/1.06 (step t2.t77.t15.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t15.t16.t28 t2.t77.t15.t16.t29))
% 0.85/1.06 (step t2.t77.t15.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t16.t30 t2.t77.t15.t16.t31))
% 0.85/1.06 (step t2.t77.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t15 t2.t77.t15.t16))
% 0.85/1.06 (step t2.t77.t15.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t19.t4 t2.t77.t15.t19.t5))
% 0.85/1.06 (step t2.t77.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t19.t8.t3 t2.t77.t15.t19.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t19.t7 t2.t77.t15.t19.t8))
% 0.85/1.06 (step t2.t77.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t19.t6 t2.t77.t15.t19.t9))
% 0.85/1.06 (step t2.t77.t15.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t15.t19.t10 t2.t77.t15.t19.t11))
% 0.85/1.06 (step t2.t77.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t15.t19.t12 t2.t77.t15.t19.t13))
% 0.85/1.06 (step t2.t77.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t19.t14 t2.t77.t15.t19.t15))
% 0.85/1.06 (step t2.t77.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t19.t16 t2.t77.t15.t19.t17))
% 0.85/1.06 (step t2.t77.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t18 t2.t77.t15.t19))
% 0.85/1.06 (step t2.t77.t15.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t17 t2.t77.t15.t20))
% 0.85/1.06 (step t2.t77.t15.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t14 t2.t77.t15.t21 a6))
% 0.85/1.06 (step t2.t77.t15.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t25.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t25.t7.t5))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t25.t7.t6 t2.t77.t15.t25.t7.t8))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t25.t7.t7 t2.t77.t15.t25.t7.t9))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t25.t7.t6 t2.t77.t15.t25.t7.t11))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t25.t7.t10 t2.t77.t15.t25.t7.t12))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t25.t7.t6 t2.t77.t15.t25.t7.t13))
% 0.85/1.06 (step t2.t77.t15.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t25.t7.t14 t2.t77.t15.t25.t7.t15))
% 0.85/1.06 (step t2.t77.t15.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t25.t6 t2.t77.t15.t25.t7))
% 0.85/1.06 (step t2.t77.t15.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t25.t10.t5 t2.t77.t15.t25.t10.t6))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t25.t10.t9.t3 t2.t77.t15.t25.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t25.t10.t8 t2.t77.t15.t25.t10.t9))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t25.t10.t7 t2.t77.t15.t25.t10.t10))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t25.t10.t11 t2.t77.t15.t25.t10.t12))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t25.t10.t15.t2 t2.t77.t15.t25.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t25.t10.t14 t2.t77.t15.t25.t10.t15))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t25.t10.t13 t2.t77.t15.t25.t10.t16))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t25.t10.t4 t2.t77.t15.t25.t10.t17))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t25.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t25.t10.t19 t2.t77.t15.t25.t10.t20))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t25.t10.t18 t2.t77.t15.t25.t10.t21))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t25.t10.t22 t2.t77.t15.t25.t10.t23))
% 0.85/1.06 (step t2.t77.t15.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t25.t10.t24 t2.t77.t15.t25.t10.t25))
% 0.85/1.06 (step t2.t77.t15.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t25.t9 t2.t77.t15.t25.t10))
% 0.85/1.06 (step t2.t77.t15.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t25.t8 t2.t77.t15.t25.t11))
% 0.85/1.06 (step t2.t77.t15.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t25.t5 t2.t77.t15.t25.t12 a4))
% 0.85/1.06 (step t2.t77.t15.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t25.t4 t2.t77.t15.t25.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t25.t14))
% 0.85/1.06 (step t2.t77.t15.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t25.t14))
% 0.85/1.06 (step t2.t77.t15.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t25.t16 t2.t77.t15.t25.t17))
% 0.85/1.06 (step t2.t77.t15.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t25.t15 t2.t77.t15.t25.t18))
% 0.85/1.06 (step t2.t77.t15.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t15.t25.t19 t2.t77.t15.t25.t20))
% 0.85/1.06 (step t2.t77.t15.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t25.t21 t2.t77.t15.t25.t22))
% 0.85/1.06 (step t2.t77.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t24 t2.t77.t15.t25))
% 0.85/1.06 (step t2.t77.t15.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t28.t4 t2.t77.t15.t28.t5))
% 0.85/1.06 (step t2.t77.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t28.t8.t3 t2.t77.t15.t28.t8.t4))
% 0.85/1.06 (step t2.t77.t15.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t28.t7 t2.t77.t15.t28.t8))
% 0.85/1.06 (step t2.t77.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t28.t6 t2.t77.t15.t28.t9))
% 0.85/1.06 (step t2.t77.t15.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t15.t28.t10 t2.t77.t15.t28.t11))
% 0.85/1.06 (step t2.t77.t15.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t28.t12 t2.t77.t15.t28.t13))
% 0.85/1.06 (step t2.t77.t15.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t28.t14 t2.t77.t15.t28.t15))
% 0.85/1.06 (step t2.t77.t15.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t15.t28.t16 t2.t77.t15.t28.t17))
% 0.85/1.06 (step t2.t77.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t15.t27 t2.t77.t15.t28))
% 0.85/1.06 (step t2.t77.t15.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t26 t2.t77.t15.t29))
% 0.85/1.06 (step t2.t77.t15.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t15.t23 t2.t77.t15.t30 a5))
% 0.85/1.06 (step t2.t77.t15.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t15.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t15.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t34.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t34.t5))
% 0.85/1.06 (step t2.t77.t15.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t15.t34.t5))
% 0.85/1.06 (step t2.t77.t15.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t15.t34.t6 t2.t77.t15.t34.t8))
% 0.85/1.06 (step t2.t77.t15.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t15.t34.t7 t2.t77.t15.t34.t9))
% 0.85/1.06 (step t2.t77.t15.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t15.t34.t6 t2.t77.t15.t34.t11))
% 0.85/1.06 (step t2.t77.t15.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t15.t34.t10 t2.t77.t15.t34.t12))
% 0.85/1.06 (step t2.t77.t15.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t15.t34.t6 t2.t77.t15.t34.t13))
% 0.85/1.06 (step t2.t77.t15.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t34.t14 t2.t77.t15.t34.t15))
% 0.85/1.06 (step t2.t77.t15.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t15.t33 t2.t77.t15.t34))
% 0.85/1.06 (step t2.t77.t15.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t15.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t15.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t15.t37.t5 t2.t77.t15.t37.t6))
% 0.85/1.06 (step t2.t77.t15.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t15.t37.t9.t3 t2.t77.t15.t37.t9.t4))
% 0.85/1.06 (step t2.t77.t15.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t37.t8 t2.t77.t15.t37.t9))
% 0.85/1.06 (step t2.t77.t15.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t15.t37.t7 t2.t77.t15.t37.t10))
% 0.85/1.06 (step t2.t77.t15.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t37.t11 t2.t77.t15.t37.t12))
% 0.85/1.06 (step t2.t77.t15.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t15.t37.t15.t2 t2.t77.t15.t37.t15.t3))
% 0.85/1.06 (step t2.t77.t15.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t37.t14 t2.t77.t15.t37.t15))
% 0.85/1.06 (step t2.t77.t15.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t15.t37.t13 t2.t77.t15.t37.t16))
% 0.85/1.06 (step t2.t77.t15.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t15.t37.t4 t2.t77.t15.t37.t17))
% 0.85/1.06 (step t2.t77.t15.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t15.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t15.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t15.t37.t20.t2))
% 0.85/1.06 (step t2.t77.t15.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t37.t19 t2.t77.t15.t37.t20))
% 0.85/1.06 (step t2.t77.t15.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t15.t37.t18 t2.t77.t15.t37.t21))
% 0.85/1.06 (step t2.t77.t15.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t37.t22 t2.t77.t15.t37.t23))
% 0.85/1.06 (step t2.t77.t15.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t15.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t15.t37.t24 t2.t77.t15.t37.t25))
% 0.85/1.06 (step t2.t77.t15.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t15.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t15.t36 t2.t77.t15.t37))
% 0.85/1.06 (step t2.t77.t15.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t15.t35 t2.t77.t15.t38))
% 0.85/1.06 (step t2.t77.t15.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t15.t32 t2.t77.t15.t39 a4))
% 0.85/1.06 (step t2.t77.t15.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t15.t4 t2.t77.t15.t13 t2.t77.t15.t22 t2.t77.t15.t31 t2.t77.t15.t40 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t15.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t15.t41))
% 0.85/1.06 (step t2.t77.t15.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t77.t15.t41))
% 0.85/1.06 (step t2.t77.t15.t44 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t77.t15.t43 t2.t77.t15.t44))
% 0.85/1.06 (step t2.t77.t15.t46 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t77.t15.t45 t2.t77.t15.t46))
% 0.85/1.06 (step t2.t77.t15.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t77.t15.t42 t2.t77.t15.t47))
% 0.85/1.06 (step t2.t77.t15.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t15.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t77.t15.t48 t2.t77.t15.t49))
% 0.85/1.06 (step t2.t77.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t16 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t14 t2.t77.t15))
% 0.85/1.06 (step t2.t77.t17 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t77.t18.t5 t2.t77.t18.t6))
% 0.85/1.06 (step t2.t77.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t18.t7 t2.t77.t18.t8))
% 0.85/1.06 (step t2.t77.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t18.t4 t2.t77.t18.t9))
% 0.85/1.06 (step t2.t77.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t18.t12 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t18.t12.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t18.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t77.t18.t12.t2))
% 0.85/1.06 (step t2.t77.t18.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t18.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t77.t18.t12.t3 t2.t77.t18.t12.t4))
% 0.85/1.06 (step t2.t77.t18.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t77.t18.t11 t2.t77.t18.t12))
% 0.85/1.06 (step t2.t77.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t77.t18.t10 t2.t77.t18.t13))
% 0.85/1.06 (step t2.t77.t18.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t18.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t18.t14 t2.t77.t18.t15))
% 0.85/1.06 (step t2.t77.t18.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t18.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t18.t16 t2.t77.t18.t17))
% 0.85/1.06 (step t2.t77.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t19 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t17 t2.t77.t18))
% 0.85/1.06 (step t2.t77.t20 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t16 t2.t77.t19))
% 0.85/1.06 (step t2.t77.t21 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t13 t2.t77.t20 a8))
% 0.85/1.06 (step t2.t77.t22 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t23 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t7.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t7.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t6 t2.t77.t24.t7.t7.t7.t8))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t7 t2.t77.t24.t7.t7.t7.t9))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t6 t2.t77.t24.t7.t7.t7.t11))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t10 t2.t77.t24.t7.t7.t7.t12))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t6 t2.t77.t24.t7.t7.t7.t13))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t7.t7.t14 t2.t77.t24.t7.t7.t7.t15))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t7.t7.t6 t2.t77.t24.t7.t7.t7))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t5 t2.t77.t24.t7.t7.t10.t6))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t9.t3 t2.t77.t24.t7.t7.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t8 t2.t77.t24.t7.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t7 t2.t77.t24.t7.t7.t10.t10))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t11 t2.t77.t24.t7.t7.t10.t12))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t15.t2 t2.t77.t24.t7.t7.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t14 t2.t77.t24.t7.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t13 t2.t77.t24.t7.t7.t10.t16))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t4 t2.t77.t24.t7.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t19 t2.t77.t24.t7.t7.t10.t20))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t18 t2.t77.t24.t7.t7.t10.t21))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t7.t10.t22 t2.t77.t24.t7.t7.t10.t23))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t7.t7.t10.t24 t2.t77.t24.t7.t7.t10.t25))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t24.t7.t7.t9 t2.t77.t24.t7.t7.t10))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t24.t7.t7.t8 t2.t77.t24.t7.t7.t11))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t24.t7.t7.t5 t2.t77.t24.t7.t7.t12 a4))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t7.t7.t4 t2.t77.t24.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t7.t7.t14))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t7.t7.t14))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t7.t7.t16 t2.t77.t24.t7.t7.t17))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t7.t7.t15 t2.t77.t24.t7.t7.t18))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t24.t7.t7.t19 t2.t77.t24.t7.t7.t20))
% 0.85/1.06 (step t2.t77.t24.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t7.t21 t2.t77.t24.t7.t7.t22))
% 0.85/1.06 (step t2.t77.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t7.t6 t2.t77.t24.t7.t7))
% 0.85/1.06 (step t2.t77.t24.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t7.t10.t4 t2.t77.t24.t7.t10.t5))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t7.t10.t8.t3 t2.t77.t24.t7.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t10.t7 t2.t77.t24.t7.t10.t8))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t10.t6 t2.t77.t24.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t24.t7.t10.t10 t2.t77.t24.t7.t10.t11))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t10.t12 t2.t77.t24.t7.t10.t13))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t10.t14 t2.t77.t24.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t24.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t24.t7.t10.t16 t2.t77.t24.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t24.t7.t9 t2.t77.t24.t7.t10))
% 0.85/1.06 (step t2.t77.t24.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t7.t8 t2.t77.t24.t7.t11))
% 0.85/1.06 (step t2.t77.t24.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t24.t7.t5 t2.t77.t24.t7.t12 a5))
% 0.85/1.06 (step t2.t77.t24.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t7.t16.t5))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t7.t16.t5))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t7.t16.t6 t2.t77.t24.t7.t16.t8))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t7.t16.t7 t2.t77.t24.t7.t16.t9))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t24.t7.t16.t6 t2.t77.t24.t7.t16.t11))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t24.t7.t16.t10 t2.t77.t24.t7.t16.t12))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t24.t7.t16.t6 t2.t77.t24.t7.t16.t13))
% 0.85/1.06 (step t2.t77.t24.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t16.t14 t2.t77.t24.t7.t16.t15))
% 0.85/1.06 (step t2.t77.t24.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t7.t15 t2.t77.t24.t7.t16))
% 0.85/1.06 (step t2.t77.t24.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t7.t19.t5 t2.t77.t24.t7.t19.t6))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t7.t19.t9.t3 t2.t77.t24.t7.t19.t9.t4))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t19.t8 t2.t77.t24.t7.t19.t9))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t7.t19.t7 t2.t77.t24.t7.t19.t10))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t7.t19.t11 t2.t77.t24.t7.t19.t12))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t24.t7.t19.t15.t2 t2.t77.t24.t7.t19.t15.t3))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t7.t19.t14 t2.t77.t24.t7.t19.t15))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t7.t19.t13 t2.t77.t24.t7.t19.t16))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t24.t7.t19.t4 t2.t77.t24.t7.t19.t17))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t7.t19.t20.t2))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t7.t19.t19 t2.t77.t24.t7.t19.t20))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t7.t19.t18 t2.t77.t24.t7.t19.t21))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t19.t22 t2.t77.t24.t7.t19.t23))
% 0.85/1.06 (step t2.t77.t24.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t7.t19.t24 t2.t77.t24.t7.t19.t25))
% 0.85/1.06 (step t2.t77.t24.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t24.t7.t18 t2.t77.t24.t7.t19))
% 0.85/1.06 (step t2.t77.t24.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t24.t7.t17 t2.t77.t24.t7.t20))
% 0.85/1.06 (step t2.t77.t24.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t24.t7.t14 t2.t77.t24.t7.t21 a4))
% 0.85/1.06 (step t2.t77.t24.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t7.t4 t2.t77.t24.t7.t13 t2.t77.t24.t7.t22 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t7.t23))
% 0.85/1.06 (step t2.t77.t24.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t7.t23))
% 0.85/1.06 (step t2.t77.t24.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t24.t7.t25 t2.t77.t24.t7.t26))
% 0.85/1.06 (step t2.t77.t24.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t24.t7.t24 t2.t77.t24.t7.t27))
% 0.85/1.06 (step t2.t77.t24.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t24.t7.t28 t2.t77.t24.t7.t29))
% 0.85/1.06 (step t2.t77.t24.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t7.t30 t2.t77.t24.t7.t31))
% 0.85/1.06 (step t2.t77.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t6 t2.t77.t24.t7))
% 0.85/1.06 (step t2.t77.t24.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t10.t4 t2.t77.t24.t10.t5))
% 0.85/1.06 (step t2.t77.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t10.t8.t3 t2.t77.t24.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t10.t7 t2.t77.t24.t10.t8))
% 0.85/1.06 (step t2.t77.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t10.t6 t2.t77.t24.t10.t9))
% 0.85/1.06 (step t2.t77.t24.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t24.t10.t10 t2.t77.t24.t10.t11))
% 0.85/1.06 (step t2.t77.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t24.t10.t12 t2.t77.t24.t10.t13))
% 0.85/1.06 (step t2.t77.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t10.t14 t2.t77.t24.t10.t15))
% 0.85/1.06 (step t2.t77.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t24.t10.t16 t2.t77.t24.t10.t17))
% 0.85/1.06 (step t2.t77.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t24.t9 t2.t77.t24.t10))
% 0.85/1.06 (step t2.t77.t24.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t8 t2.t77.t24.t11))
% 0.85/1.06 (step t2.t77.t24.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t24.t5 t2.t77.t24.t12 a6))
% 0.85/1.06 (step t2.t77.t24.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t16.t7.t5))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t16.t7.t5))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t16.t7.t6 t2.t77.t24.t16.t7.t8))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t16.t7.t7 t2.t77.t24.t16.t7.t9))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t24.t16.t7.t6 t2.t77.t24.t16.t7.t11))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t24.t16.t7.t10 t2.t77.t24.t16.t7.t12))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t24.t16.t7.t6 t2.t77.t24.t16.t7.t13))
% 0.85/1.06 (step t2.t77.t24.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t16.t7.t14 t2.t77.t24.t16.t7.t15))
% 0.85/1.06 (step t2.t77.t24.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t16.t6 t2.t77.t24.t16.t7))
% 0.85/1.06 (step t2.t77.t24.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t16.t10.t5 t2.t77.t24.t16.t10.t6))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t16.t10.t9.t3 t2.t77.t24.t16.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t16.t10.t8 t2.t77.t24.t16.t10.t9))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t16.t10.t7 t2.t77.t24.t16.t10.t10))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t16.t10.t11 t2.t77.t24.t16.t10.t12))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t24.t16.t10.t15.t2 t2.t77.t24.t16.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t16.t10.t14 t2.t77.t24.t16.t10.t15))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t16.t10.t13 t2.t77.t24.t16.t10.t16))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t24.t16.t10.t4 t2.t77.t24.t16.t10.t17))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t16.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t16.t10.t19 t2.t77.t24.t16.t10.t20))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t16.t10.t18 t2.t77.t24.t16.t10.t21))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t16.t10.t22 t2.t77.t24.t16.t10.t23))
% 0.85/1.06 (step t2.t77.t24.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t16.t10.t24 t2.t77.t24.t16.t10.t25))
% 0.85/1.06 (step t2.t77.t24.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t24.t16.t9 t2.t77.t24.t16.t10))
% 0.85/1.06 (step t2.t77.t24.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t24.t16.t8 t2.t77.t24.t16.t11))
% 0.85/1.06 (step t2.t77.t24.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t24.t16.t5 t2.t77.t24.t16.t12 a4))
% 0.85/1.06 (step t2.t77.t24.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t16.t4 t2.t77.t24.t16.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t16.t14))
% 0.85/1.06 (step t2.t77.t24.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t16.t14))
% 0.85/1.06 (step t2.t77.t24.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t16.t16 t2.t77.t24.t16.t17))
% 0.85/1.06 (step t2.t77.t24.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t16.t15 t2.t77.t24.t16.t18))
% 0.85/1.06 (step t2.t77.t24.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t24.t16.t19 t2.t77.t24.t16.t20))
% 0.85/1.06 (step t2.t77.t24.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t16.t21 t2.t77.t24.t16.t22))
% 0.85/1.06 (step t2.t77.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t15 t2.t77.t24.t16))
% 0.85/1.06 (step t2.t77.t24.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t19.t4 t2.t77.t24.t19.t5))
% 0.85/1.06 (step t2.t77.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t19.t8.t3 t2.t77.t24.t19.t8.t4))
% 0.85/1.06 (step t2.t77.t24.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t19.t7 t2.t77.t24.t19.t8))
% 0.85/1.06 (step t2.t77.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t19.t6 t2.t77.t24.t19.t9))
% 0.85/1.06 (step t2.t77.t24.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t24.t19.t10 t2.t77.t24.t19.t11))
% 0.85/1.06 (step t2.t77.t24.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t19.t12 t2.t77.t24.t19.t13))
% 0.85/1.06 (step t2.t77.t24.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t19.t14 t2.t77.t24.t19.t15))
% 0.85/1.06 (step t2.t77.t24.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t24.t19.t16 t2.t77.t24.t19.t17))
% 0.85/1.06 (step t2.t77.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t24.t18 t2.t77.t24.t19))
% 0.85/1.06 (step t2.t77.t24.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t17 t2.t77.t24.t20))
% 0.85/1.06 (step t2.t77.t24.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t24.t14 t2.t77.t24.t21 a5))
% 0.85/1.06 (step t2.t77.t24.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t24.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t24.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t25.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t24.t25.t5))
% 0.85/1.06 (step t2.t77.t24.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t24.t25.t5))
% 0.85/1.06 (step t2.t77.t24.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t24.t25.t6 t2.t77.t24.t25.t8))
% 0.85/1.06 (step t2.t77.t24.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t24.t25.t7 t2.t77.t24.t25.t9))
% 0.85/1.06 (step t2.t77.t24.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t24.t25.t6 t2.t77.t24.t25.t11))
% 0.85/1.06 (step t2.t77.t24.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t24.t25.t10 t2.t77.t24.t25.t12))
% 0.85/1.06 (step t2.t77.t24.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t24.t25.t6 t2.t77.t24.t25.t13))
% 0.85/1.06 (step t2.t77.t24.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t25.t14 t2.t77.t24.t25.t15))
% 0.85/1.06 (step t2.t77.t24.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t24.t24 t2.t77.t24.t25))
% 0.85/1.06 (step t2.t77.t24.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t24.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t24.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t24.t28.t5 t2.t77.t24.t28.t6))
% 0.85/1.06 (step t2.t77.t24.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t24.t28.t9.t3 t2.t77.t24.t28.t9.t4))
% 0.85/1.06 (step t2.t77.t24.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t28.t8 t2.t77.t24.t28.t9))
% 0.85/1.06 (step t2.t77.t24.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t24.t28.t7 t2.t77.t24.t28.t10))
% 0.85/1.06 (step t2.t77.t24.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t28.t11 t2.t77.t24.t28.t12))
% 0.85/1.06 (step t2.t77.t24.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t24.t28.t15.t2 t2.t77.t24.t28.t15.t3))
% 0.85/1.06 (step t2.t77.t24.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t28.t14 t2.t77.t24.t28.t15))
% 0.85/1.06 (step t2.t77.t24.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t24.t28.t13 t2.t77.t24.t28.t16))
% 0.85/1.06 (step t2.t77.t24.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t24.t28.t4 t2.t77.t24.t28.t17))
% 0.85/1.06 (step t2.t77.t24.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t24.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t24.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t24.t28.t20.t2))
% 0.85/1.06 (step t2.t77.t24.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t28.t19 t2.t77.t24.t28.t20))
% 0.85/1.06 (step t2.t77.t24.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t24.t28.t18 t2.t77.t24.t28.t21))
% 0.85/1.06 (step t2.t77.t24.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t28.t22 t2.t77.t24.t28.t23))
% 0.85/1.06 (step t2.t77.t24.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t24.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t24.t28.t24 t2.t77.t24.t28.t25))
% 0.85/1.06 (step t2.t77.t24.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t24.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t24.t27 t2.t77.t24.t28))
% 0.85/1.06 (step t2.t77.t24.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t24.t26 t2.t77.t24.t29))
% 0.85/1.06 (step t2.t77.t24.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t24.t23 t2.t77.t24.t30 a4))
% 0.85/1.06 (step t2.t77.t24.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t24.t4 t2.t77.t24.t13 t2.t77.t24.t22 t2.t77.t24.t31 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t24.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t77.t24.t32))
% 0.85/1.06 (step t2.t77.t24.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t77.t24.t32))
% 0.85/1.06 (step t2.t77.t24.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t24.t34 t2.t77.t24.t35))
% 0.85/1.06 (step t2.t77.t24.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t77.t24.t36 t2.t77.t24.t37))
% 0.85/1.06 (step t2.t77.t24.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t77.t24.t33 t2.t77.t24.t38))
% 0.85/1.06 (step t2.t77.t24.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t24.t34 t2.t77.t24.t37))
% 0.85/1.06 (step t2.t77.t24.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t77.t24.t40 t2.t77.t24.t35))
% 0.85/1.06 (step t2.t77.t24.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t77.t24.t39 t2.t77.t24.t41))
% 0.85/1.06 (step t2.t77.t24.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t24.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t77.t24.t42 t2.t77.t24.t43))
% 0.85/1.06 (step t2.t77.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t25 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t77.t23 t2.t77.t24))
% 0.85/1.06 (step t2.t77.t26 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t77.t27.t5 t2.t77.t27.t6))
% 0.85/1.06 (step t2.t77.t27.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t77.t27.t7 t2.t77.t27.t8))
% 0.85/1.06 (step t2.t77.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t27.t4 t2.t77.t27.t9))
% 0.85/1.06 (step t2.t77.t27.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t27.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t27.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t27.t12.t3))
% 0.85/1.06 (step t2.t77.t27.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t77.t27.t12.t4 t2.t77.t27.t12.t5))
% 0.85/1.06 (step t2.t77.t27.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t27.t12.t6))
% 0.85/1.06 (step t2.t77.t27.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t27.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t27.t11 t2.t77.t27.t12))
% 0.85/1.06 (step t2.t77.t27.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t77.t27.t10 t2.t77.t27.t13))
% 0.85/1.06 (step t2.t77.t27.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t77.t27.t15 t2.t77.t27.t16))
% 0.85/1.06 (step t2.t77.t27.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t77.t27.t17 t2.t77.t27.t18))
% 0.85/1.06 (step t2.t77.t27.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t27.t14 t2.t77.t27.t19))
% 0.85/1.06 (step t2.t77.t27.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t27.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t27.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t77.t27.t22.t3))
% 0.85/1.06 (step t2.t77.t27.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t27.t22.t2 t2.t77.t27.t22.t4))
% 0.85/1.06 (step t2.t77.t27.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t77.t27.t22.t5))
% 0.85/1.06 (step t2.t77.t27.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t27.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t27.t21 t2.t77.t27.t22))
% 0.85/1.06 (step t2.t77.t27.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t27.t20 t2.t77.t27.t23))
% 0.85/1.06 (step t2.t77.t27.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t27.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t77.t27.t24 t2.t77.t27.t25))
% 0.85/1.06 (step t2.t77.t27.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t27.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t77.t27.t26 t2.t77.t27.t27))
% 0.85/1.06 (step t2.t77.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t28 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t77.t26 t2.t77.t27))
% 0.85/1.06 (step t2.t77.t29 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t77.t25 t2.t77.t28))
% 0.85/1.06 (step t2.t77.t30 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t77.t22 t2.t77.t29 a7))
% 0.85/1.06 (step t2.t77.t31 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t32 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t33.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t33.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t33.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t33.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t33.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t33.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t33.t7.t7.t5))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t33.t7.t7.t6 t2.t77.t33.t7.t7.t8))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t33.t7.t7.t7 t2.t77.t33.t7.t7.t9))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t33.t7.t7.t6 t2.t77.t33.t7.t7.t11))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t33.t7.t7.t10 t2.t77.t33.t7.t7.t12))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t33.t7.t7.t6 t2.t77.t33.t7.t7.t13))
% 0.85/1.06 (step t2.t77.t33.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t7.t7.t14 t2.t77.t33.t7.t7.t15))
% 0.85/1.06 (step t2.t77.t33.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t33.t7.t6 t2.t77.t33.t7.t7))
% 0.85/1.06 (step t2.t77.t33.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t33.t7.t10.t5 t2.t77.t33.t7.t10.t6))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t33.t7.t10.t9.t3 t2.t77.t33.t7.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t7.t10.t8 t2.t77.t33.t7.t10.t9))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t7.t10.t7 t2.t77.t33.t7.t10.t10))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t33.t7.t10.t11 t2.t77.t33.t7.t10.t12))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t33.t7.t10.t15.t2 t2.t77.t33.t7.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t33.t7.t10.t14 t2.t77.t33.t7.t10.t15))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t33.t7.t10.t13 t2.t77.t33.t7.t10.t16))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t33.t7.t10.t4 t2.t77.t33.t7.t10.t17))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t33.t7.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t33.t7.t10.t19 t2.t77.t33.t7.t10.t20))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t33.t7.t10.t18 t2.t77.t33.t7.t10.t21))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t7.t10.t22 t2.t77.t33.t7.t10.t23))
% 0.85/1.06 (step t2.t77.t33.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t33.t7.t10.t24 t2.t77.t33.t7.t10.t25))
% 0.85/1.06 (step t2.t77.t33.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t33.t7.t9 t2.t77.t33.t7.t10))
% 0.85/1.06 (step t2.t77.t33.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t33.t7.t8 t2.t77.t33.t7.t11))
% 0.85/1.06 (step t2.t77.t33.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t33.t7.t5 t2.t77.t33.t7.t12 a4))
% 0.85/1.06 (step t2.t77.t33.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t33.t7.t4 t2.t77.t33.t7.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t33.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t33.t7.t14))
% 0.85/1.06 (step t2.t77.t33.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t33.t7.t14))
% 0.85/1.06 (step t2.t77.t33.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t33.t7.t16 t2.t77.t33.t7.t17))
% 0.85/1.06 (step t2.t77.t33.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t33.t7.t15 t2.t77.t33.t7.t18))
% 0.85/1.06 (step t2.t77.t33.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t33.t7.t19 t2.t77.t33.t7.t20))
% 0.85/1.06 (step t2.t77.t33.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t7.t21 t2.t77.t33.t7.t22))
% 0.85/1.06 (step t2.t77.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t33.t6 t2.t77.t33.t7))
% 0.85/1.06 (step t2.t77.t33.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t33.t10.t4 t2.t77.t33.t10.t5))
% 0.85/1.06 (step t2.t77.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t33.t10.t8.t3 t2.t77.t33.t10.t8.t4))
% 0.85/1.06 (step t2.t77.t33.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t10.t7 t2.t77.t33.t10.t8))
% 0.85/1.06 (step t2.t77.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t10.t6 t2.t77.t33.t10.t9))
% 0.85/1.06 (step t2.t77.t33.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t33.t10.t10 t2.t77.t33.t10.t11))
% 0.85/1.06 (step t2.t77.t33.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t10.t12 t2.t77.t33.t10.t13))
% 0.85/1.06 (step t2.t77.t33.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t10.t14 t2.t77.t33.t10.t15))
% 0.85/1.06 (step t2.t77.t33.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t33.t10.t16 t2.t77.t33.t10.t17))
% 0.85/1.06 (step t2.t77.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t33.t9 t2.t77.t33.t10))
% 0.85/1.06 (step t2.t77.t33.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t33.t8 t2.t77.t33.t11))
% 0.85/1.06 (step t2.t77.t33.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t33.t5 t2.t77.t33.t12 a5))
% 0.85/1.06 (step t2.t77.t33.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t33.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t33.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t33.t16.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t33.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t33.t16.t5))
% 0.85/1.06 (step t2.t77.t33.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t33.t16.t5))
% 0.85/1.06 (step t2.t77.t33.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t33.t16.t6 t2.t77.t33.t16.t8))
% 0.85/1.06 (step t2.t77.t33.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t33.t16.t7 t2.t77.t33.t16.t9))
% 0.85/1.06 (step t2.t77.t33.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t33.t16.t6 t2.t77.t33.t16.t11))
% 0.85/1.06 (step t2.t77.t33.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t33.t16.t10 t2.t77.t33.t16.t12))
% 0.85/1.06 (step t2.t77.t33.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t33.t16.t6 t2.t77.t33.t16.t13))
% 0.85/1.06 (step t2.t77.t33.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t16.t14 t2.t77.t33.t16.t15))
% 0.85/1.06 (step t2.t77.t33.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t33.t15 t2.t77.t33.t16))
% 0.85/1.06 (step t2.t77.t33.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t33.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t33.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t33.t19.t5 t2.t77.t33.t19.t6))
% 0.85/1.06 (step t2.t77.t33.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t33.t19.t9.t3 t2.t77.t33.t19.t9.t4))
% 0.85/1.06 (step t2.t77.t33.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t19.t8 t2.t77.t33.t19.t9))
% 0.85/1.06 (step t2.t77.t33.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t33.t19.t7 t2.t77.t33.t19.t10))
% 0.85/1.06 (step t2.t77.t33.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t33.t19.t11 t2.t77.t33.t19.t12))
% 0.85/1.06 (step t2.t77.t33.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t33.t19.t15.t2 t2.t77.t33.t19.t15.t3))
% 0.85/1.06 (step t2.t77.t33.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t33.t19.t14 t2.t77.t33.t19.t15))
% 0.85/1.06 (step t2.t77.t33.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t33.t19.t13 t2.t77.t33.t19.t16))
% 0.85/1.06 (step t2.t77.t33.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t33.t19.t4 t2.t77.t33.t19.t17))
% 0.85/1.06 (step t2.t77.t33.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t33.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t33.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t33.t19.t20.t2))
% 0.85/1.06 (step t2.t77.t33.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t33.t19.t19 t2.t77.t33.t19.t20))
% 0.85/1.06 (step t2.t77.t33.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t33.t19.t18 t2.t77.t33.t19.t21))
% 0.85/1.06 (step t2.t77.t33.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t19.t22 t2.t77.t33.t19.t23))
% 0.85/1.06 (step t2.t77.t33.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t33.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t33.t19.t24 t2.t77.t33.t19.t25))
% 0.85/1.06 (step t2.t77.t33.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t33.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t33.t18 t2.t77.t33.t19))
% 0.85/1.06 (step t2.t77.t33.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t33.t17 t2.t77.t33.t20))
% 0.85/1.06 (step t2.t77.t33.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t33.t14 t2.t77.t33.t21 a4))
% 0.85/1.06 (step t2.t77.t33.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t33.t4 t2.t77.t33.t13 t2.t77.t33.t22 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t33.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t33.t23))
% 0.85/1.06 (step t2.t77.t33.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t33.t23))
% 0.85/1.06 (step t2.t77.t33.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t33.t25 t2.t77.t33.t26))
% 0.85/1.06 (step t2.t77.t33.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t33.t24 t2.t77.t33.t27))
% 0.85/1.06 (step t2.t77.t33.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t77.t33.t28 t2.t77.t33.t29))
% 0.85/1.06 (step t2.t77.t33.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t33.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t77.t33.t30 t2.t77.t33.t31))
% 0.85/1.06 (step t2.t77.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t34 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t77.t32 t2.t77.t33))
% 0.85/1.06 (step t2.t77.t35 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t36.t4 t2.t77.t36.t5))
% 0.85/1.06 (step t2.t77.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t36.t8.t3 t2.t77.t36.t8.t4))
% 0.85/1.06 (step t2.t77.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t36.t7 t2.t77.t36.t8))
% 0.85/1.06 (step t2.t77.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t36.t6 t2.t77.t36.t9))
% 0.85/1.06 (step t2.t77.t36.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t77.t36.t10 t2.t77.t36.t11))
% 0.85/1.06 (step t2.t77.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t77.t36.t12 t2.t77.t36.t13))
% 0.85/1.06 (step t2.t77.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t36.t14 t2.t77.t36.t15))
% 0.85/1.06 (step t2.t77.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t77.t36.t16 t2.t77.t36.t17))
% 0.85/1.06 (step t2.t77.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t37 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t77.t35 t2.t77.t36))
% 0.85/1.06 (step t2.t77.t38 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t77.t34 t2.t77.t37))
% 0.85/1.06 (step t2.t77.t39 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t77.t31 t2.t77.t38 a6))
% 0.85/1.06 (step t2.t77.t40 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t41 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t42.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t42.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t42.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t42.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t42.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t42.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t42.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t42.t7.t5))
% 0.85/1.06 (step t2.t77.t42.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t42.t7.t5))
% 0.85/1.06 (step t2.t77.t42.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t42.t7.t6 t2.t77.t42.t7.t8))
% 0.85/1.06 (step t2.t77.t42.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t42.t7.t7 t2.t77.t42.t7.t9))
% 0.85/1.06 (step t2.t77.t42.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t42.t7.t6 t2.t77.t42.t7.t11))
% 0.85/1.06 (step t2.t77.t42.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t42.t7.t10 t2.t77.t42.t7.t12))
% 0.85/1.06 (step t2.t77.t42.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t42.t7.t6 t2.t77.t42.t7.t13))
% 0.85/1.06 (step t2.t77.t42.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t42.t7.t14 t2.t77.t42.t7.t15))
% 0.85/1.06 (step t2.t77.t42.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t42.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t42.t6 t2.t77.t42.t7))
% 0.85/1.06 (step t2.t77.t42.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t42.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t42.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t42.t10.t5 t2.t77.t42.t10.t6))
% 0.85/1.06 (step t2.t77.t42.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t42.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t42.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t42.t10.t9.t3 t2.t77.t42.t10.t9.t4))
% 0.85/1.06 (step t2.t77.t42.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t42.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t42.t10.t8 t2.t77.t42.t10.t9))
% 0.85/1.06 (step t2.t77.t42.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t42.t10.t7 t2.t77.t42.t10.t10))
% 0.85/1.06 (step t2.t77.t42.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t42.t10.t11 t2.t77.t42.t10.t12))
% 0.85/1.06 (step t2.t77.t42.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t42.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t42.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t42.t10.t15.t2 t2.t77.t42.t10.t15.t3))
% 0.85/1.06 (step t2.t77.t42.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t42.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t42.t10.t14 t2.t77.t42.t10.t15))
% 0.85/1.06 (step t2.t77.t42.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t42.t10.t13 t2.t77.t42.t10.t16))
% 0.85/1.06 (step t2.t77.t42.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t42.t10.t4 t2.t77.t42.t10.t17))
% 0.85/1.06 (step t2.t77.t42.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t42.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t42.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t42.t10.t20.t2))
% 0.85/1.06 (step t2.t77.t42.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t42.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t42.t10.t19 t2.t77.t42.t10.t20))
% 0.85/1.06 (step t2.t77.t42.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t42.t10.t18 t2.t77.t42.t10.t21))
% 0.85/1.06 (step t2.t77.t42.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t42.t10.t22 t2.t77.t42.t10.t23))
% 0.85/1.06 (step t2.t77.t42.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t42.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t42.t10.t24 t2.t77.t42.t10.t25))
% 0.85/1.06 (step t2.t77.t42.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t42.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t42.t9 t2.t77.t42.t10))
% 0.85/1.06 (step t2.t77.t42.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t42.t8 t2.t77.t42.t11))
% 0.85/1.06 (step t2.t77.t42.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t42.t5 t2.t77.t42.t12 a4))
% 0.85/1.06 (step t2.t77.t42.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t42.t4 t2.t77.t42.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t42.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t42.t14))
% 0.85/1.06 (step t2.t77.t42.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t42.t14))
% 0.85/1.06 (step t2.t77.t42.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t42.t16 t2.t77.t42.t17))
% 0.85/1.06 (step t2.t77.t42.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t42.t15 t2.t77.t42.t18))
% 0.85/1.06 (step t2.t77.t42.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t77.t42.t19 t2.t77.t42.t20))
% 0.85/1.06 (step t2.t77.t42.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t42.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t77.t42.t21 t2.t77.t42.t22))
% 0.85/1.06 (step t2.t77.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t43 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t77.t41 t2.t77.t42))
% 0.85/1.06 (step t2.t77.t44 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t45.t4 t2.t77.t45.t5))
% 0.85/1.06 (step t2.t77.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t45.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t45.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t45.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t45.t8.t3 t2.t77.t45.t8.t4))
% 0.85/1.06 (step t2.t77.t45.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t45.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t45.t7 t2.t77.t45.t8))
% 0.85/1.06 (step t2.t77.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t45.t6 t2.t77.t45.t9))
% 0.85/1.06 (step t2.t77.t45.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t77.t45.t10 t2.t77.t45.t11))
% 0.85/1.06 (step t2.t77.t45.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t45.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t45.t12 t2.t77.t45.t13))
% 0.85/1.06 (step t2.t77.t45.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t45.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t77.t45.t14 t2.t77.t45.t15))
% 0.85/1.06 (step t2.t77.t45.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t45.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t77.t45.t16 t2.t77.t45.t17))
% 0.85/1.06 (step t2.t77.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t77.t46 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t77.t44 t2.t77.t45))
% 0.85/1.06 (step t2.t77.t47 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t43 t2.t77.t46))
% 0.85/1.06 (step t2.t77.t48 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t77.t40 t2.t77.t47 a5))
% 0.85/1.06 (step t2.t77.t49 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t77.t50 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t51 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t51.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t77.t51.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t51.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t51.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t51.t5))
% 0.85/1.06 (step t2.t77.t51.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t77.t51.t5))
% 0.85/1.06 (step t2.t77.t51.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t77.t51.t6 t2.t77.t51.t8))
% 0.85/1.06 (step t2.t77.t51.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t77.t51.t7 t2.t77.t51.t9))
% 0.85/1.06 (step t2.t77.t51.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t77.t51.t6 t2.t77.t51.t11))
% 0.85/1.06 (step t2.t77.t51.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t77.t51.t10 t2.t77.t51.t12))
% 0.85/1.06 (step t2.t77.t51.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t77.t51.t6 t2.t77.t51.t13))
% 0.85/1.06 (step t2.t77.t51.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t51.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t77.t51.t14 t2.t77.t51.t15))
% 0.85/1.06 (step t2.t77.t51 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t52 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t77.t50 t2.t77.t51))
% 0.85/1.06 (step t2.t77.t53 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t77.t54 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t54.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t77.t54.t5 t2.t77.t54.t6))
% 0.85/1.06 (step t2.t77.t54.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t54.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t54.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t77.t54.t9.t3 t2.t77.t54.t9.t4))
% 0.85/1.06 (step t2.t77.t54.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t77.t54.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t54.t8 t2.t77.t54.t9))
% 0.85/1.06 (step t2.t77.t54.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t77.t54.t7 t2.t77.t54.t10))
% 0.85/1.06 (step t2.t77.t54.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t54.t11 t2.t77.t54.t12))
% 0.85/1.06 (step t2.t77.t54.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t54.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t54.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t77.t54.t15.t2 t2.t77.t54.t15.t3))
% 0.85/1.06 (step t2.t77.t54.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t77.t54.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t54.t14 t2.t77.t54.t15))
% 0.85/1.06 (step t2.t77.t54.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t77.t54.t13 t2.t77.t54.t16))
% 0.85/1.06 (step t2.t77.t54.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t77.t54.t4 t2.t77.t54.t17))
% 0.85/1.06 (step t2.t77.t54.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t77.t54.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t77.t54.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t77.t54.t20.t2))
% 0.85/1.06 (step t2.t77.t54.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t54.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t54.t19 t2.t77.t54.t20))
% 0.85/1.06 (step t2.t77.t54.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t77.t54.t18 t2.t77.t54.t21))
% 0.85/1.06 (step t2.t77.t54.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t54.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t77.t54.t22 t2.t77.t54.t23))
% 0.85/1.06 (step t2.t77.t54.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t77.t54.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t77.t54.t24 t2.t77.t54.t25))
% 0.85/1.06 (step t2.t77.t54 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t77.t55 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t77.t53 t2.t77.t54))
% 0.85/1.06 (step t2.t77.t56 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t77.t52 t2.t77.t55))
% 0.85/1.06 (step t2.t77.t57 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t77.t49 t2.t77.t56 a4))
% 0.85/1.06 (step t2.t77.t58 (cl (and (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t77.t3 t2.t77.t12 a10 a9 t2.t77.t21 t2.t77.t30 t2.t77.t39 t2.t77.t48 t2.t77.t57 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t77.t59 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t77.t58))
% 0.85/1.06 (step t2.t77.t60 (cl (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule and :premises (t2.t77.t58))
% 0.85/1.06 (anchor :step t2.t77.t61 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t77.t61.t1 (cl (= P P)) :rule refl)
% 0.85/1.06 (step t2.t77.t61.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t61.t3 (cl (= (@ Phi P) (@ Phi P))) :rule refl)
% 0.85/1.06 (step t2.t77.t61.t4 (cl (= (@ tptp.mnot (@ Phi P)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)))) :rule cong :premises (t2.t77.t59 t2.t77.t61.t3))
% 0.85/1.06 (step t2.t77.t61.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t61.t6 (cl (= (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) :rule cong :premises (t2.t77.t61.t4 t2.t77.t61.t5))
% 0.85/1.06 (step t2.t77.t61 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t77.t62 (cl (= (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))))) :rule cong :premises (t2.t77.t60 t2.t77.t61))
% 0.85/1.06 (step t2.t77.t63 (cl (= (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))))) :rule cong :premises (t2.t77.t59 t2.t77.t62))
% 0.85/1.06 (step t2.t77.t64 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t77.t65 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t77.t63 t2.t77.t64))
% 0.85/1.06 (step t2.t77 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t78 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t76 t2.t77))
% 0.85/1.06 (step t2.t79 (cl (= tptp.mexists_prop tptp.mexists_prop)) :rule refl)
% 0.85/1.06 (anchor :step t2.t80 :args ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t80.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t80.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t80.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t80.t4 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule refl)
% 0.85/1.06 (anchor :step t2.t80.t5 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t80.t5.t1 (cl (= P P)) :rule refl)
% 0.85/1.06 (step t2.t80.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t80.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t80.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))) __flatten_var_0))) :rule cong :premises (t2.t80.t5.t3 t2.t80.t5.t4))
% 0.85/1.06 (step t2.t80.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi P) W))) __flatten_var_0) (not (@ (@ Phi P) __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0) (not (@ (@ Phi P) __flatten_var_0)))) :rule trans :premises (t2.t80.t5.t5 t2.t80.t5.t6))
% 0.85/1.06 (step t2.t80.t5 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t80.t6 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))))) :rule cong :premises (t2.t80.t4 t2.t80.t5))
% 0.85/1.06 (step t2.t80.t7 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t80.t8 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t80.t8.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (anchor :step t2.t80.t8.t2 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.85/1.06 (step t2.t80.t8.t2.t1 (cl (= P P)) :rule refl)
% 0.85/1.06 (step t2.t80.t8.t2.t2 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t80.t8.t2.t4 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) W))) :rule cong :premises (t2.t80.t8.t2.t2 t2.t80.t8.t2.t3))
% 0.85/1.06 (step t2.t80.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) W) (not (@ (@ Phi P) W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t8.t2.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W) (not (@ (@ Phi P) W)))) :rule trans :premises (t2.t80.t8.t2.t4 t2.t80.t8.t2.t5))
% 0.85/1.06 (step t2.t80.t8.t2 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) :rule bind)
% 0.85/1.06 (step t2.t80.t8 (cl (= (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0))) P) W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule bind)
% 0.85/1.06 (step t2.t80.t9 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi P) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule trans :premises (t2.t80.t7 t2.t80.t8))
% 0.85/1.06 (step t2.t80.t10 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule trans :premises (t2.t80.t6 t2.t80.t9))
% 0.85/1.06 (step t2.t80.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule cong :premises (t2.t80.t3 t2.t80.t10))
% 0.85/1.06 (step t2.t80.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t80.t13 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t80.t13.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t80.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))))) :rule cong :premises (t2.t80.t13.t2))
% 0.85/1.06 (step t2.t80.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule bind)
% 0.85/1.06 (step t2.t80.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule trans :premises (t2.t80.t12 t2.t80.t13))
% 0.85/1.06 (step t2.t80.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))))) :rule trans :premises (t2.t80.t11 t2.t80.t14))
% 0.85/1.06 (step t2.t80.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t80.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) __flatten_var_0))) :rule cong :premises (t2.t80.t15 t2.t80.t16))
% 0.85/1.06 (step t2.t80.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) W))))) __flatten_var_0) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t80.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) :rule trans :premises (t2.t80.t17 t2.t80.t18))
% 0.85/1.06 (step t2.t80 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t81 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) :rule cong :premises (t2.t79 t2.t80))
% 0.85/1.06 (step t2.t82 (cl (= (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))))) :rule trans :premises (t2.t78 t2.t81))
% 0.85/1.06 (step t2.t83 (cl (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0))))))) :rule resolution :premises (t2.t75 t2.t82 a12))
% 0.85/1.06 (step t2.t84 (cl (not (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) (not (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t85 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t3 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) (not (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t4 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t5 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t7.t7.t7.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t7.t7.t7.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t6 t2.t86.t6.t7.t7.t7.t7.t8))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t7 t2.t86.t6.t7.t7.t7.t7.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t6 t2.t86.t6.t7.t7.t7.t7.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t10 t2.t86.t6.t7.t7.t7.t7.t12))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t6 t2.t86.t6.t7.t7.t7.t7.t13))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t7.t14 t2.t86.t6.t7.t7.t7.t7.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t6 t2.t86.t6.t7.t7.t7.t7))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t5 t2.t86.t6.t7.t7.t7.t10.t6))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t9.t3 t2.t86.t6.t7.t7.t7.t10.t9.t4))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t8 t2.t86.t6.t7.t7.t7.t10.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t7 t2.t86.t6.t7.t7.t7.t10.t10))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t11 t2.t86.t6.t7.t7.t7.t10.t12))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t15.t2 t2.t86.t6.t7.t7.t7.t10.t15.t3))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t14 t2.t86.t6.t7.t7.t7.t10.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t13 t2.t86.t6.t7.t7.t7.t10.t16))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t4 t2.t86.t6.t7.t7.t7.t10.t17))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t20.t2))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t19 t2.t86.t6.t7.t7.t7.t10.t20))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t18 t2.t86.t6.t7.t7.t7.t10.t21))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t10.t22 t2.t86.t6.t7.t7.t7.t10.t23))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t10.t24 t2.t86.t6.t7.t7.t7.t10.t25))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t9 t2.t86.t6.t7.t7.t7.t10))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t7.t7.t7.t8 t2.t86.t6.t7.t7.t7.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t7.t7.t7.t5 t2.t86.t6.t7.t7.t7.t12 a4))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t7.t7.t4 t2.t86.t6.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t7.t7.t14))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t7.t7.t14))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t16 t2.t86.t6.t7.t7.t7.t17))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t15 t2.t86.t6.t7.t7.t7.t18))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t19 t2.t86.t6.t7.t7.t7.t20))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t7.t21 t2.t86.t6.t7.t7.t7.t22))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t7.t6 t2.t86.t6.t7.t7.t7))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t10.t4 t2.t86.t6.t7.t7.t10.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t7.t10.t8.t3 t2.t86.t6.t7.t7.t10.t8.t4))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t10.t7 t2.t86.t6.t7.t7.t10.t8))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t10.t6 t2.t86.t6.t7.t7.t10.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t7.t10.t10 t2.t86.t6.t7.t7.t10.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t10.t12 t2.t86.t6.t7.t7.t10.t13))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t10.t14 t2.t86.t6.t7.t7.t10.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t7.t7.t10.t16 t2.t86.t6.t7.t7.t10.t17))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t7.t7.t9 t2.t86.t6.t7.t7.t10))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t7.t8 t2.t86.t6.t7.t7.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t7.t7.t5 t2.t86.t6.t7.t7.t12 a5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t7.t16.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t7.t16.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t6 t2.t86.t6.t7.t7.t16.t8))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t7 t2.t86.t6.t7.t7.t16.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t6 t2.t86.t6.t7.t7.t16.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t10 t2.t86.t6.t7.t7.t16.t12))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t6 t2.t86.t6.t7.t7.t16.t13))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t16.t14 t2.t86.t6.t7.t7.t16.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t7.t15 t2.t86.t6.t7.t7.t16))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t5 t2.t86.t6.t7.t7.t19.t6))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t9.t3 t2.t86.t6.t7.t7.t19.t9.t4))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t8 t2.t86.t6.t7.t7.t19.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t7 t2.t86.t6.t7.t7.t19.t10))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t11 t2.t86.t6.t7.t7.t19.t12))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t15.t2 t2.t86.t6.t7.t7.t19.t15.t3))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t14 t2.t86.t6.t7.t7.t19.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t13 t2.t86.t6.t7.t7.t19.t16))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t4 t2.t86.t6.t7.t7.t19.t17))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t20.t2))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t19 t2.t86.t6.t7.t7.t19.t20))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t18 t2.t86.t6.t7.t7.t19.t21))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t19.t22 t2.t86.t6.t7.t7.t19.t23))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t7.t19.t24 t2.t86.t6.t7.t7.t19.t25))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t7.t7.t18 t2.t86.t6.t7.t7.t19))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t7.t7.t17 t2.t86.t6.t7.t7.t20))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t7.t7.t14 t2.t86.t6.t7.t7.t21 a4))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t7.t4 t2.t86.t6.t7.t7.t13 t2.t86.t6.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t7.t23))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t7.t23))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t7.t25 t2.t86.t6.t7.t7.t26))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t7.t7.t24 t2.t86.t6.t7.t7.t27))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t86.t6.t7.t7.t28 t2.t86.t6.t7.t7.t29))
% 0.85/1.06 (step t2.t86.t6.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t7.t30 t2.t86.t6.t7.t7.t31))
% 0.85/1.06 (step t2.t86.t6.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t6 t2.t86.t6.t7.t7))
% 0.85/1.06 (step t2.t86.t6.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t10.t4 t2.t86.t6.t7.t10.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t10.t8.t3 t2.t86.t6.t7.t10.t8.t4))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t10.t7 t2.t86.t6.t7.t10.t8))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t10.t6 t2.t86.t6.t7.t10.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t10.t10 t2.t86.t6.t7.t10.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t86.t6.t7.t10.t12 t2.t86.t6.t7.t10.t13))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t10.t14 t2.t86.t6.t7.t10.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t7.t10.t16 t2.t86.t6.t7.t10.t17))
% 0.85/1.06 (step t2.t86.t6.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t7.t9 t2.t86.t6.t7.t10))
% 0.85/1.06 (step t2.t86.t6.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t8 t2.t86.t6.t7.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t7.t5 t2.t86.t6.t7.t12 a6))
% 0.85/1.06 (step t2.t86.t6.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t16.t7.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t16.t7.t5))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t6 t2.t86.t6.t7.t16.t7.t8))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t7 t2.t86.t6.t7.t16.t7.t9))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t6 t2.t86.t6.t7.t16.t7.t11))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t10 t2.t86.t6.t7.t16.t7.t12))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t6 t2.t86.t6.t7.t16.t7.t13))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t16.t7.t14 t2.t86.t6.t7.t16.t7.t15))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t16.t6 t2.t86.t6.t7.t16.t7))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t5 t2.t86.t6.t7.t16.t10.t6))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.06 (anchor :step t2.t86.t6.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.06 (step t2.t86.t6.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t9.t3 t2.t86.t6.t7.t16.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t8 t2.t86.t6.t7.t16.t10.t9))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t7 t2.t86.t6.t7.t16.t10.t10))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t11 t2.t86.t6.t7.t16.t10.t12))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t15.t2 t2.t86.t6.t7.t16.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t14 t2.t86.t6.t7.t16.t10.t15))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t13 t2.t86.t6.t7.t16.t10.t16))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t4 t2.t86.t6.t7.t16.t10.t17))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t19 t2.t86.t6.t7.t16.t10.t20))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t18 t2.t86.t6.t7.t16.t10.t21))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t16.t10.t22 t2.t86.t6.t7.t16.t10.t23))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t16.t10.t24 t2.t86.t6.t7.t16.t10.t25))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t7.t16.t9 t2.t86.t6.t7.t16.t10))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t7.t16.t8 t2.t86.t6.t7.t16.t11))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t7.t16.t5 t2.t86.t6.t7.t16.t12 a4))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t16.t4 t2.t86.t6.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t16.t14))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t16.t14))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t16.t16 t2.t86.t6.t7.t16.t17))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t16.t15 t2.t86.t6.t7.t16.t18))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t6.t7.t16.t19 t2.t86.t6.t7.t16.t20))
% 0.85/1.07 (step t2.t86.t6.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t16.t21 t2.t86.t6.t7.t16.t22))
% 0.85/1.07 (step t2.t86.t6.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t15 t2.t86.t6.t7.t16))
% 0.85/1.07 (step t2.t86.t6.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t19.t4 t2.t86.t6.t7.t19.t5))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t19.t8.t3 t2.t86.t6.t7.t19.t8.t4))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t19.t7 t2.t86.t6.t7.t19.t8))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t19.t6 t2.t86.t6.t7.t19.t9))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t19.t10 t2.t86.t6.t7.t19.t11))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t19.t12 t2.t86.t6.t7.t19.t13))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t19.t14 t2.t86.t6.t7.t19.t15))
% 0.85/1.07 (step t2.t86.t6.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t7.t19.t16 t2.t86.t6.t7.t19.t17))
% 0.85/1.07 (step t2.t86.t6.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t7.t18 t2.t86.t6.t7.t19))
% 0.85/1.07 (step t2.t86.t6.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t17 t2.t86.t6.t7.t20))
% 0.85/1.07 (step t2.t86.t6.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t7.t14 t2.t86.t6.t7.t21 a5))
% 0.85/1.07 (step t2.t86.t6.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t7.t25.t5))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t7.t25.t5))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t7.t25.t6 t2.t86.t6.t7.t25.t8))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t7.t25.t7 t2.t86.t6.t7.t25.t9))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t7.t25.t6 t2.t86.t6.t7.t25.t11))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t7.t25.t10 t2.t86.t6.t7.t25.t12))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t7.t25.t6 t2.t86.t6.t7.t25.t13))
% 0.85/1.07 (step t2.t86.t6.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t25.t14 t2.t86.t6.t7.t25.t15))
% 0.85/1.07 (step t2.t86.t6.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t7.t24 t2.t86.t6.t7.t25))
% 0.85/1.07 (step t2.t86.t6.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t7.t28.t5 t2.t86.t6.t7.t28.t6))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t7.t28.t9.t3 t2.t86.t6.t7.t28.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t28.t8 t2.t86.t6.t7.t28.t9))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t7.t28.t7 t2.t86.t6.t7.t28.t10))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t28.t11 t2.t86.t6.t7.t28.t12))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t7.t28.t15.t2 t2.t86.t6.t7.t28.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t28.t14 t2.t86.t6.t7.t28.t15))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t7.t28.t13 t2.t86.t6.t7.t28.t16))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t7.t28.t4 t2.t86.t6.t7.t28.t17))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t7.t28.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t28.t19 t2.t86.t6.t7.t28.t20))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t7.t28.t18 t2.t86.t6.t7.t28.t21))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t28.t22 t2.t86.t6.t7.t28.t23))
% 0.85/1.07 (step t2.t86.t6.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t7.t28.t24 t2.t86.t6.t7.t28.t25))
% 0.85/1.07 (step t2.t86.t6.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t7.t27 t2.t86.t6.t7.t28))
% 0.85/1.07 (step t2.t86.t6.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t7.t26 t2.t86.t6.t7.t29))
% 0.85/1.07 (step t2.t86.t6.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t7.t23 t2.t86.t6.t7.t30 a4))
% 0.85/1.07 (step t2.t86.t6.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t7.t4 t2.t86.t6.t7.t13 t2.t86.t6.t7.t22 t2.t86.t6.t7.t31 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t86.t6.t7.t32))
% 0.85/1.07 (step t2.t86.t6.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t86.t6.t7.t32))
% 0.85/1.07 (step t2.t86.t6.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t86.t6.t7.t34 t2.t86.t6.t7.t35))
% 0.85/1.07 (step t2.t86.t6.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t86.t6.t7.t36 t2.t86.t6.t7.t37))
% 0.85/1.07 (step t2.t86.t6.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t86.t6.t7.t33 t2.t86.t6.t7.t38))
% 0.85/1.07 (step t2.t86.t6.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t86.t6.t7.t34 t2.t86.t6.t7.t37))
% 0.85/1.07 (step t2.t86.t6.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t86.t6.t7.t40 t2.t86.t6.t7.t35))
% 0.85/1.07 (step t2.t86.t6.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t86.t6.t7.t39 t2.t86.t6.t7.t41))
% 0.85/1.07 (step t2.t86.t6.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t7.t42 t2.t86.t6.t7.t43))
% 0.85/1.07 (step t2.t86.t6.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t6 t2.t86.t6.t7))
% 0.85/1.07 (step t2.t86.t6.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t86.t6.t10.t5 t2.t86.t6.t10.t6))
% 0.85/1.07 (step t2.t86.t6.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t86.t6.t10.t7 t2.t86.t6.t10.t8))
% 0.85/1.07 (step t2.t86.t6.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t10.t4 t2.t86.t6.t10.t9))
% 0.85/1.07 (step t2.t86.t6.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t10.t12.t3))
% 0.85/1.07 (step t2.t86.t6.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t10.t12.t4 t2.t86.t6.t10.t12.t5))
% 0.85/1.07 (step t2.t86.t6.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t10.t12.t6))
% 0.85/1.07 (step t2.t86.t6.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t86.t6.t10.t11 t2.t86.t6.t10.t12))
% 0.85/1.07 (step t2.t86.t6.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t86.t6.t10.t10 t2.t86.t6.t10.t13))
% 0.85/1.07 (step t2.t86.t6.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t86.t6.t10.t15 t2.t86.t6.t10.t16))
% 0.85/1.07 (step t2.t86.t6.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t86.t6.t10.t17 t2.t86.t6.t10.t18))
% 0.85/1.07 (step t2.t86.t6.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t10.t14 t2.t86.t6.t10.t19))
% 0.85/1.07 (step t2.t86.t6.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t10.t22.t3))
% 0.85/1.07 (step t2.t86.t6.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t10.t22.t2 t2.t86.t6.t10.t22.t4))
% 0.85/1.07 (step t2.t86.t6.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t86.t6.t10.t22.t5))
% 0.85/1.07 (step t2.t86.t6.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t10.t21 t2.t86.t6.t10.t22))
% 0.85/1.07 (step t2.t86.t6.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t10.t20 t2.t86.t6.t10.t23))
% 0.85/1.07 (step t2.t86.t6.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t10.t24 t2.t86.t6.t10.t25))
% 0.85/1.07 (step t2.t86.t6.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t86.t6.t10.t26 t2.t86.t6.t10.t27))
% 0.85/1.07 (step t2.t86.t6.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t86.t6.t9 t2.t86.t6.t10))
% 0.85/1.07 (step t2.t86.t6.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t86.t6.t8 t2.t86.t6.t11))
% 0.85/1.07 (step t2.t86.t6.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t86.t6.t5 t2.t86.t6.t12 a7))
% 0.85/1.07 (step t2.t86.t6.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t16.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t16.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t6 t2.t86.t6.t16.t7.t7.t8))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t7 t2.t86.t6.t16.t7.t7.t9))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t6 t2.t86.t6.t16.t7.t7.t11))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t10 t2.t86.t6.t16.t7.t7.t12))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t6 t2.t86.t6.t16.t7.t7.t13))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t7.t7.t14 t2.t86.t6.t16.t7.t7.t15))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t16.t7.t6 t2.t86.t6.t16.t7.t7))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t5 t2.t86.t6.t16.t7.t10.t6))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t9.t3 t2.t86.t6.t16.t7.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t8 t2.t86.t6.t16.t7.t10.t9))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t7 t2.t86.t6.t16.t7.t10.t10))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t11 t2.t86.t6.t16.t7.t10.t12))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t15.t2 t2.t86.t6.t16.t7.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t14 t2.t86.t6.t16.t7.t10.t15))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t13 t2.t86.t6.t16.t7.t10.t16))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t4 t2.t86.t6.t16.t7.t10.t17))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t19 t2.t86.t6.t16.t7.t10.t20))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t18 t2.t86.t6.t16.t7.t10.t21))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t7.t10.t22 t2.t86.t6.t16.t7.t10.t23))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t16.t7.t10.t24 t2.t86.t6.t16.t7.t10.t25))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t16.t7.t9 t2.t86.t6.t16.t7.t10))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t16.t7.t8 t2.t86.t6.t16.t7.t11))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t16.t7.t5 t2.t86.t6.t16.t7.t12 a4))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t16.t7.t4 t2.t86.t6.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t16.t7.t14))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t16.t7.t14))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t16.t7.t16 t2.t86.t6.t16.t7.t17))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t16.t7.t15 t2.t86.t6.t16.t7.t18))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t6.t16.t7.t19 t2.t86.t6.t16.t7.t20))
% 0.85/1.07 (step t2.t86.t6.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t7.t21 t2.t86.t6.t16.t7.t22))
% 0.85/1.07 (step t2.t86.t6.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t16.t6 t2.t86.t6.t16.t7))
% 0.85/1.07 (step t2.t86.t6.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t16.t10.t4 t2.t86.t6.t16.t10.t5))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t16.t10.t8.t3 t2.t86.t6.t16.t10.t8.t4))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t10.t7 t2.t86.t6.t16.t10.t8))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t10.t6 t2.t86.t6.t16.t10.t9))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t6.t16.t10.t10 t2.t86.t6.t16.t10.t11))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t10.t12 t2.t86.t6.t16.t10.t13))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t10.t14 t2.t86.t6.t16.t10.t15))
% 0.85/1.07 (step t2.t86.t6.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t16.t10.t16 t2.t86.t6.t16.t10.t17))
% 0.85/1.07 (step t2.t86.t6.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t16.t9 t2.t86.t6.t16.t10))
% 0.85/1.07 (step t2.t86.t6.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t16.t8 t2.t86.t6.t16.t11))
% 0.85/1.07 (step t2.t86.t6.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t16.t5 t2.t86.t6.t16.t12 a5))
% 0.85/1.07 (step t2.t86.t6.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t16.t16.t5))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t16.t16.t5))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t16.t16.t6 t2.t86.t6.t16.t16.t8))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t16.t16.t7 t2.t86.t6.t16.t16.t9))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t16.t16.t6 t2.t86.t6.t16.t16.t11))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t16.t16.t10 t2.t86.t6.t16.t16.t12))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t16.t16.t6 t2.t86.t6.t16.t16.t13))
% 0.85/1.07 (step t2.t86.t6.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t16.t14 t2.t86.t6.t16.t16.t15))
% 0.85/1.07 (step t2.t86.t6.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t16.t15 t2.t86.t6.t16.t16))
% 0.85/1.07 (step t2.t86.t6.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t16.t19.t5 t2.t86.t6.t16.t19.t6))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t16.t19.t9.t3 t2.t86.t6.t16.t19.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t19.t8 t2.t86.t6.t16.t19.t9))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t16.t19.t7 t2.t86.t6.t16.t19.t10))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t16.t19.t11 t2.t86.t6.t16.t19.t12))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t16.t19.t15.t2 t2.t86.t6.t16.t19.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t16.t19.t14 t2.t86.t6.t16.t19.t15))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t16.t19.t13 t2.t86.t6.t16.t19.t16))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t16.t19.t4 t2.t86.t6.t16.t19.t17))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t16.t19.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t16.t19.t19 t2.t86.t6.t16.t19.t20))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t16.t19.t18 t2.t86.t6.t16.t19.t21))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t19.t22 t2.t86.t6.t16.t19.t23))
% 0.85/1.07 (step t2.t86.t6.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t16.t19.t24 t2.t86.t6.t16.t19.t25))
% 0.85/1.07 (step t2.t86.t6.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t16.t18 t2.t86.t6.t16.t19))
% 0.85/1.07 (step t2.t86.t6.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t16.t17 t2.t86.t6.t16.t20))
% 0.85/1.07 (step t2.t86.t6.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t16.t14 t2.t86.t6.t16.t21 a4))
% 0.85/1.07 (step t2.t86.t6.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t16.t4 t2.t86.t6.t16.t13 t2.t86.t6.t16.t22 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t16.t23))
% 0.85/1.07 (step t2.t86.t6.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t16.t23))
% 0.85/1.07 (step t2.t86.t6.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t16.t25 t2.t86.t6.t16.t26))
% 0.85/1.07 (step t2.t86.t6.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t16.t24 t2.t86.t6.t16.t27))
% 0.85/1.07 (step t2.t86.t6.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t86.t6.t16.t28 t2.t86.t6.t16.t29))
% 0.85/1.07 (step t2.t86.t6.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t16.t30 t2.t86.t6.t16.t31))
% 0.85/1.07 (step t2.t86.t6.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t15 t2.t86.t6.t16))
% 0.85/1.07 (step t2.t86.t6.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t19.t4 t2.t86.t6.t19.t5))
% 0.85/1.07 (step t2.t86.t6.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t19.t8.t3 t2.t86.t6.t19.t8.t4))
% 0.85/1.07 (step t2.t86.t6.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t19.t7 t2.t86.t6.t19.t8))
% 0.85/1.07 (step t2.t86.t6.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t19.t6 t2.t86.t6.t19.t9))
% 0.85/1.07 (step t2.t86.t6.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t86.t6.t19.t10 t2.t86.t6.t19.t11))
% 0.85/1.07 (step t2.t86.t6.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t86.t6.t19.t12 t2.t86.t6.t19.t13))
% 0.85/1.07 (step t2.t86.t6.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t19.t14 t2.t86.t6.t19.t15))
% 0.85/1.07 (step t2.t86.t6.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t19.t16 t2.t86.t6.t19.t17))
% 0.85/1.07 (step t2.t86.t6.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t18 t2.t86.t6.t19))
% 0.85/1.07 (step t2.t86.t6.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t17 t2.t86.t6.t20))
% 0.85/1.07 (step t2.t86.t6.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t14 t2.t86.t6.t21 a6))
% 0.85/1.07 (step t2.t86.t6.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t25.t7.t5))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t25.t7.t5))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t25.t7.t6 t2.t86.t6.t25.t7.t8))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t25.t7.t7 t2.t86.t6.t25.t7.t9))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t25.t7.t6 t2.t86.t6.t25.t7.t11))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t25.t7.t10 t2.t86.t6.t25.t7.t12))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t25.t7.t6 t2.t86.t6.t25.t7.t13))
% 0.85/1.07 (step t2.t86.t6.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t25.t7.t14 t2.t86.t6.t25.t7.t15))
% 0.85/1.07 (step t2.t86.t6.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t25.t6 t2.t86.t6.t25.t7))
% 0.85/1.07 (step t2.t86.t6.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t25.t10.t5 t2.t86.t6.t25.t10.t6))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t25.t10.t9.t3 t2.t86.t6.t25.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t25.t10.t8 t2.t86.t6.t25.t10.t9))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t25.t10.t7 t2.t86.t6.t25.t10.t10))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t25.t10.t11 t2.t86.t6.t25.t10.t12))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t25.t10.t15.t2 t2.t86.t6.t25.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t25.t10.t14 t2.t86.t6.t25.t10.t15))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t25.t10.t13 t2.t86.t6.t25.t10.t16))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t25.t10.t4 t2.t86.t6.t25.t10.t17))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t25.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t25.t10.t19 t2.t86.t6.t25.t10.t20))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t25.t10.t18 t2.t86.t6.t25.t10.t21))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t25.t10.t22 t2.t86.t6.t25.t10.t23))
% 0.85/1.07 (step t2.t86.t6.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t25.t10.t24 t2.t86.t6.t25.t10.t25))
% 0.85/1.07 (step t2.t86.t6.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t25.t9 t2.t86.t6.t25.t10))
% 0.85/1.07 (step t2.t86.t6.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t25.t8 t2.t86.t6.t25.t11))
% 0.85/1.07 (step t2.t86.t6.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t25.t5 t2.t86.t6.t25.t12 a4))
% 0.85/1.07 (step t2.t86.t6.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t25.t4 t2.t86.t6.t25.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t25.t14))
% 0.85/1.07 (step t2.t86.t6.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t25.t14))
% 0.85/1.07 (step t2.t86.t6.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t25.t16 t2.t86.t6.t25.t17))
% 0.85/1.07 (step t2.t86.t6.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t25.t15 t2.t86.t6.t25.t18))
% 0.85/1.07 (step t2.t86.t6.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t6.t25.t19 t2.t86.t6.t25.t20))
% 0.85/1.07 (step t2.t86.t6.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t25.t21 t2.t86.t6.t25.t22))
% 0.85/1.07 (step t2.t86.t6.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t24 t2.t86.t6.t25))
% 0.85/1.07 (step t2.t86.t6.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t28.t4 t2.t86.t6.t28.t5))
% 0.85/1.07 (step t2.t86.t6.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t28.t8.t3 t2.t86.t6.t28.t8.t4))
% 0.85/1.07 (step t2.t86.t6.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t28.t7 t2.t86.t6.t28.t8))
% 0.85/1.07 (step t2.t86.t6.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t28.t6 t2.t86.t6.t28.t9))
% 0.85/1.07 (step t2.t86.t6.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t6.t28.t10 t2.t86.t6.t28.t11))
% 0.85/1.07 (step t2.t86.t6.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t28.t12 t2.t86.t6.t28.t13))
% 0.85/1.07 (step t2.t86.t6.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t28.t14 t2.t86.t6.t28.t15))
% 0.85/1.07 (step t2.t86.t6.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t6.t28.t16 t2.t86.t6.t28.t17))
% 0.85/1.07 (step t2.t86.t6.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t6.t27 t2.t86.t6.t28))
% 0.85/1.07 (step t2.t86.t6.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t26 t2.t86.t6.t29))
% 0.85/1.07 (step t2.t86.t6.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t6.t23 t2.t86.t6.t30 a5))
% 0.85/1.07 (step t2.t86.t6.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t6.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t6.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t34.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t34.t5))
% 0.85/1.07 (step t2.t86.t6.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t6.t34.t5))
% 0.85/1.07 (step t2.t86.t6.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t6.t34.t6 t2.t86.t6.t34.t8))
% 0.85/1.07 (step t2.t86.t6.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t6.t34.t7 t2.t86.t6.t34.t9))
% 0.85/1.07 (step t2.t86.t6.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t6.t34.t6 t2.t86.t6.t34.t11))
% 0.85/1.07 (step t2.t86.t6.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t6.t34.t10 t2.t86.t6.t34.t12))
% 0.85/1.07 (step t2.t86.t6.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t6.t34.t6 t2.t86.t6.t34.t13))
% 0.85/1.07 (step t2.t86.t6.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t34.t14 t2.t86.t6.t34.t15))
% 0.85/1.07 (step t2.t86.t6.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t6.t33 t2.t86.t6.t34))
% 0.85/1.07 (step t2.t86.t6.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t6.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t6.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t6.t37.t5 t2.t86.t6.t37.t6))
% 0.85/1.07 (step t2.t86.t6.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t6.t37.t9.t3 t2.t86.t6.t37.t9.t4))
% 0.85/1.07 (step t2.t86.t6.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t37.t8 t2.t86.t6.t37.t9))
% 0.85/1.07 (step t2.t86.t6.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t6.t37.t7 t2.t86.t6.t37.t10))
% 0.85/1.07 (step t2.t86.t6.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t37.t11 t2.t86.t6.t37.t12))
% 0.85/1.07 (step t2.t86.t6.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t6.t37.t15.t2 t2.t86.t6.t37.t15.t3))
% 0.85/1.07 (step t2.t86.t6.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t37.t14 t2.t86.t6.t37.t15))
% 0.85/1.07 (step t2.t86.t6.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t6.t37.t13 t2.t86.t6.t37.t16))
% 0.85/1.07 (step t2.t86.t6.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t6.t37.t4 t2.t86.t6.t37.t17))
% 0.85/1.07 (step t2.t86.t6.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t6.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t6.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t6.t37.t20.t2))
% 0.85/1.07 (step t2.t86.t6.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t37.t19 t2.t86.t6.t37.t20))
% 0.85/1.07 (step t2.t86.t6.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t6.t37.t18 t2.t86.t6.t37.t21))
% 0.85/1.07 (step t2.t86.t6.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t37.t22 t2.t86.t6.t37.t23))
% 0.85/1.07 (step t2.t86.t6.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t6.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t6.t37.t24 t2.t86.t6.t37.t25))
% 0.85/1.07 (step t2.t86.t6.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t6.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t6.t36 t2.t86.t6.t37))
% 0.85/1.07 (step t2.t86.t6.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t6.t35 t2.t86.t6.t38))
% 0.85/1.07 (step t2.t86.t6.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t6.t32 t2.t86.t6.t39 a4))
% 0.85/1.07 (step t2.t86.t6.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t6.t4 t2.t86.t6.t13 t2.t86.t6.t22 t2.t86.t6.t31 t2.t86.t6.t40 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t6.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t6.t41))
% 0.85/1.07 (step t2.t86.t6.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t86.t6.t41))
% 0.85/1.07 (step t2.t86.t6.t44 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t86.t6.t43 t2.t86.t6.t44))
% 0.85/1.07 (step t2.t86.t6.t46 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t86.t6.t45 t2.t86.t6.t46))
% 0.85/1.07 (step t2.t86.t6.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t86.t6.t42 t2.t86.t6.t47))
% 0.85/1.07 (step t2.t86.t6.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t6.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t86.t6.t48 t2.t86.t6.t49))
% 0.85/1.07 (step t2.t86.t6 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t7 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t86.t5 t2.t86.t6))
% 0.85/1.07 (step t2.t86.t8 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t9 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t9.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t9.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t86.t9.t5 t2.t86.t9.t6))
% 0.85/1.07 (step t2.t86.t9.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t9.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t9.t7 t2.t86.t9.t8))
% 0.85/1.07 (step t2.t86.t9.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t86.t9.t4 t2.t86.t9.t9))
% 0.85/1.07 (step t2.t86.t9.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t9.t12 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t9.t12.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t9.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t86.t9.t12.t2))
% 0.85/1.07 (step t2.t86.t9.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t9.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t86.t9.t12.t3 t2.t86.t9.t12.t4))
% 0.85/1.07 (step t2.t86.t9.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t9.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t86.t9.t11 t2.t86.t9.t12))
% 0.85/1.07 (step t2.t86.t9.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t86.t9.t10 t2.t86.t9.t13))
% 0.85/1.07 (step t2.t86.t9.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t9.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t9.t14 t2.t86.t9.t15))
% 0.85/1.07 (step t2.t86.t9.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t9.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t86.t9.t16 t2.t86.t9.t17))
% 0.85/1.07 (step t2.t86.t9 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t10 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t8 t2.t86.t9))
% 0.85/1.07 (step t2.t86.t11 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t7 t2.t86.t10))
% 0.85/1.07 (step t2.t86.t12 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t4 t2.t86.t11 a8))
% 0.85/1.07 (step t2.t86.t13 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t14 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t7.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t7.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t6 t2.t86.t15.t7.t7.t7.t8))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t7 t2.t86.t15.t7.t7.t7.t9))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t6 t2.t86.t15.t7.t7.t7.t11))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t10 t2.t86.t15.t7.t7.t7.t12))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t6 t2.t86.t15.t7.t7.t7.t13))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t7.t7.t14 t2.t86.t15.t7.t7.t7.t15))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t7.t7.t6 t2.t86.t15.t7.t7.t7))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t5 t2.t86.t15.t7.t7.t10.t6))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t9.t3 t2.t86.t15.t7.t7.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t8 t2.t86.t15.t7.t7.t10.t9))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t7 t2.t86.t15.t7.t7.t10.t10))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t11 t2.t86.t15.t7.t7.t10.t12))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t15.t2 t2.t86.t15.t7.t7.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t14 t2.t86.t15.t7.t7.t10.t15))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t13 t2.t86.t15.t7.t7.t10.t16))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t4 t2.t86.t15.t7.t7.t10.t17))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t19 t2.t86.t15.t7.t7.t10.t20))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t18 t2.t86.t15.t7.t7.t10.t21))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t7.t10.t22 t2.t86.t15.t7.t7.t10.t23))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t7.t7.t10.t24 t2.t86.t15.t7.t7.t10.t25))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t15.t7.t7.t9 t2.t86.t15.t7.t7.t10))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t15.t7.t7.t8 t2.t86.t15.t7.t7.t11))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t15.t7.t7.t5 t2.t86.t15.t7.t7.t12 a4))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t7.t7.t4 t2.t86.t15.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t7.t7.t14))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t7.t7.t14))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t7.t7.t16 t2.t86.t15.t7.t7.t17))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t7.t7.t15 t2.t86.t15.t7.t7.t18))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t15.t7.t7.t19 t2.t86.t15.t7.t7.t20))
% 0.85/1.07 (step t2.t86.t15.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t7.t21 t2.t86.t15.t7.t7.t22))
% 0.85/1.07 (step t2.t86.t15.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t7.t6 t2.t86.t15.t7.t7))
% 0.85/1.07 (step t2.t86.t15.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t7.t10.t4 t2.t86.t15.t7.t10.t5))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t7.t10.t8.t3 t2.t86.t15.t7.t10.t8.t4))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t10.t7 t2.t86.t15.t7.t10.t8))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t10.t6 t2.t86.t15.t7.t10.t9))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t15.t7.t10.t10 t2.t86.t15.t7.t10.t11))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t10.t12 t2.t86.t15.t7.t10.t13))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t10.t14 t2.t86.t15.t7.t10.t15))
% 0.85/1.07 (step t2.t86.t15.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t15.t7.t10.t16 t2.t86.t15.t7.t10.t17))
% 0.85/1.07 (step t2.t86.t15.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t15.t7.t9 t2.t86.t15.t7.t10))
% 0.85/1.07 (step t2.t86.t15.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t7.t8 t2.t86.t15.t7.t11))
% 0.85/1.07 (step t2.t86.t15.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t15.t7.t5 t2.t86.t15.t7.t12 a5))
% 0.85/1.07 (step t2.t86.t15.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t7.t16.t5))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t7.t16.t5))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t7.t16.t6 t2.t86.t15.t7.t16.t8))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t7.t16.t7 t2.t86.t15.t7.t16.t9))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t15.t7.t16.t6 t2.t86.t15.t7.t16.t11))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t15.t7.t16.t10 t2.t86.t15.t7.t16.t12))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t15.t7.t16.t6 t2.t86.t15.t7.t16.t13))
% 0.85/1.07 (step t2.t86.t15.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t16.t14 t2.t86.t15.t7.t16.t15))
% 0.85/1.07 (step t2.t86.t15.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t7.t15 t2.t86.t15.t7.t16))
% 0.85/1.07 (step t2.t86.t15.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t7.t19.t5 t2.t86.t15.t7.t19.t6))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t7.t19.t9.t3 t2.t86.t15.t7.t19.t9.t4))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t19.t8 t2.t86.t15.t7.t19.t9))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t7.t19.t7 t2.t86.t15.t7.t19.t10))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t7.t19.t11 t2.t86.t15.t7.t19.t12))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t15.t7.t19.t15.t2 t2.t86.t15.t7.t19.t15.t3))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t7.t19.t14 t2.t86.t15.t7.t19.t15))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t7.t19.t13 t2.t86.t15.t7.t19.t16))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t15.t7.t19.t4 t2.t86.t15.t7.t19.t17))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t7.t19.t20.t2))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t7.t19.t19 t2.t86.t15.t7.t19.t20))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t7.t19.t18 t2.t86.t15.t7.t19.t21))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t19.t22 t2.t86.t15.t7.t19.t23))
% 0.85/1.07 (step t2.t86.t15.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t7.t19.t24 t2.t86.t15.t7.t19.t25))
% 0.85/1.07 (step t2.t86.t15.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t15.t7.t18 t2.t86.t15.t7.t19))
% 0.85/1.07 (step t2.t86.t15.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t15.t7.t17 t2.t86.t15.t7.t20))
% 0.85/1.07 (step t2.t86.t15.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t15.t7.t14 t2.t86.t15.t7.t21 a4))
% 0.85/1.07 (step t2.t86.t15.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t7.t4 t2.t86.t15.t7.t13 t2.t86.t15.t7.t22 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t7.t23))
% 0.85/1.07 (step t2.t86.t15.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t7.t23))
% 0.85/1.07 (step t2.t86.t15.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t15.t7.t25 t2.t86.t15.t7.t26))
% 0.85/1.07 (step t2.t86.t15.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t15.t7.t24 t2.t86.t15.t7.t27))
% 0.85/1.07 (step t2.t86.t15.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t86.t15.t7.t28 t2.t86.t15.t7.t29))
% 0.85/1.07 (step t2.t86.t15.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t7.t30 t2.t86.t15.t7.t31))
% 0.85/1.07 (step t2.t86.t15.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t6 t2.t86.t15.t7))
% 0.85/1.07 (step t2.t86.t15.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t10.t4 t2.t86.t15.t10.t5))
% 0.85/1.07 (step t2.t86.t15.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t10.t8.t3 t2.t86.t15.t10.t8.t4))
% 0.85/1.07 (step t2.t86.t15.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t10.t7 t2.t86.t15.t10.t8))
% 0.85/1.07 (step t2.t86.t15.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t10.t6 t2.t86.t15.t10.t9))
% 0.85/1.07 (step t2.t86.t15.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t86.t15.t10.t10 t2.t86.t15.t10.t11))
% 0.85/1.07 (step t2.t86.t15.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t86.t15.t10.t12 t2.t86.t15.t10.t13))
% 0.85/1.07 (step t2.t86.t15.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t10.t14 t2.t86.t15.t10.t15))
% 0.85/1.07 (step t2.t86.t15.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t86.t15.t10.t16 t2.t86.t15.t10.t17))
% 0.85/1.07 (step t2.t86.t15.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t15.t9 t2.t86.t15.t10))
% 0.85/1.07 (step t2.t86.t15.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t8 t2.t86.t15.t11))
% 0.85/1.07 (step t2.t86.t15.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t86.t15.t5 t2.t86.t15.t12 a6))
% 0.85/1.07 (step t2.t86.t15.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t16.t7.t5))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t16.t7.t5))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t16.t7.t6 t2.t86.t15.t16.t7.t8))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t16.t7.t7 t2.t86.t15.t16.t7.t9))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t15.t16.t7.t6 t2.t86.t15.t16.t7.t11))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t15.t16.t7.t10 t2.t86.t15.t16.t7.t12))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t15.t16.t7.t6 t2.t86.t15.t16.t7.t13))
% 0.85/1.07 (step t2.t86.t15.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t16.t7.t14 t2.t86.t15.t16.t7.t15))
% 0.85/1.07 (step t2.t86.t15.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t16.t6 t2.t86.t15.t16.t7))
% 0.85/1.07 (step t2.t86.t15.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t16.t10.t5 t2.t86.t15.t16.t10.t6))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t16.t10.t9.t3 t2.t86.t15.t16.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t16.t10.t8 t2.t86.t15.t16.t10.t9))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t16.t10.t7 t2.t86.t15.t16.t10.t10))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t16.t10.t11 t2.t86.t15.t16.t10.t12))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t15.t16.t10.t15.t2 t2.t86.t15.t16.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t16.t10.t14 t2.t86.t15.t16.t10.t15))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t16.t10.t13 t2.t86.t15.t16.t10.t16))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t15.t16.t10.t4 t2.t86.t15.t16.t10.t17))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t16.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t16.t10.t19 t2.t86.t15.t16.t10.t20))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t16.t10.t18 t2.t86.t15.t16.t10.t21))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t16.t10.t22 t2.t86.t15.t16.t10.t23))
% 0.85/1.07 (step t2.t86.t15.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t16.t10.t24 t2.t86.t15.t16.t10.t25))
% 0.85/1.07 (step t2.t86.t15.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t15.t16.t9 t2.t86.t15.t16.t10))
% 0.85/1.07 (step t2.t86.t15.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t15.t16.t8 t2.t86.t15.t16.t11))
% 0.85/1.07 (step t2.t86.t15.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t15.t16.t5 t2.t86.t15.t16.t12 a4))
% 0.85/1.07 (step t2.t86.t15.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t16.t4 t2.t86.t15.t16.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t16.t14))
% 0.85/1.07 (step t2.t86.t15.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t16.t14))
% 0.85/1.07 (step t2.t86.t15.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t16.t16 t2.t86.t15.t16.t17))
% 0.85/1.07 (step t2.t86.t15.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t16.t15 t2.t86.t15.t16.t18))
% 0.85/1.07 (step t2.t86.t15.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t15.t16.t19 t2.t86.t15.t16.t20))
% 0.85/1.07 (step t2.t86.t15.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t16.t21 t2.t86.t15.t16.t22))
% 0.85/1.07 (step t2.t86.t15.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t15 t2.t86.t15.t16))
% 0.85/1.07 (step t2.t86.t15.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t19.t4 t2.t86.t15.t19.t5))
% 0.85/1.07 (step t2.t86.t15.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t19.t8.t3 t2.t86.t15.t19.t8.t4))
% 0.85/1.07 (step t2.t86.t15.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t19.t7 t2.t86.t15.t19.t8))
% 0.85/1.07 (step t2.t86.t15.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t19.t6 t2.t86.t15.t19.t9))
% 0.85/1.07 (step t2.t86.t15.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t15.t19.t10 t2.t86.t15.t19.t11))
% 0.85/1.07 (step t2.t86.t15.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t19.t12 t2.t86.t15.t19.t13))
% 0.85/1.07 (step t2.t86.t15.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t19.t14 t2.t86.t15.t19.t15))
% 0.85/1.07 (step t2.t86.t15.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t15.t19.t16 t2.t86.t15.t19.t17))
% 0.85/1.07 (step t2.t86.t15.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t15.t18 t2.t86.t15.t19))
% 0.85/1.07 (step t2.t86.t15.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t17 t2.t86.t15.t20))
% 0.85/1.07 (step t2.t86.t15.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t15.t14 t2.t86.t15.t21 a5))
% 0.85/1.07 (step t2.t86.t15.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t15.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t15.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t25.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t15.t25.t5))
% 0.85/1.07 (step t2.t86.t15.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t15.t25.t5))
% 0.85/1.07 (step t2.t86.t15.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t15.t25.t6 t2.t86.t15.t25.t8))
% 0.85/1.07 (step t2.t86.t15.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t15.t25.t7 t2.t86.t15.t25.t9))
% 0.85/1.07 (step t2.t86.t15.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t15.t25.t6 t2.t86.t15.t25.t11))
% 0.85/1.07 (step t2.t86.t15.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t15.t25.t10 t2.t86.t15.t25.t12))
% 0.85/1.07 (step t2.t86.t15.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t15.t25.t6 t2.t86.t15.t25.t13))
% 0.85/1.07 (step t2.t86.t15.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t25.t14 t2.t86.t15.t25.t15))
% 0.85/1.07 (step t2.t86.t15.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t15.t24 t2.t86.t15.t25))
% 0.85/1.07 (step t2.t86.t15.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t15.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t15.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t15.t28.t5 t2.t86.t15.t28.t6))
% 0.85/1.07 (step t2.t86.t15.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t15.t28.t9.t3 t2.t86.t15.t28.t9.t4))
% 0.85/1.07 (step t2.t86.t15.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t28.t8 t2.t86.t15.t28.t9))
% 0.85/1.07 (step t2.t86.t15.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t15.t28.t7 t2.t86.t15.t28.t10))
% 0.85/1.07 (step t2.t86.t15.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t28.t11 t2.t86.t15.t28.t12))
% 0.85/1.07 (step t2.t86.t15.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t15.t28.t15.t2 t2.t86.t15.t28.t15.t3))
% 0.85/1.07 (step t2.t86.t15.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t28.t14 t2.t86.t15.t28.t15))
% 0.85/1.07 (step t2.t86.t15.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t15.t28.t13 t2.t86.t15.t28.t16))
% 0.85/1.07 (step t2.t86.t15.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t15.t28.t4 t2.t86.t15.t28.t17))
% 0.85/1.07 (step t2.t86.t15.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t15.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t15.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t15.t28.t20.t2))
% 0.85/1.07 (step t2.t86.t15.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t28.t19 t2.t86.t15.t28.t20))
% 0.85/1.07 (step t2.t86.t15.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t15.t28.t18 t2.t86.t15.t28.t21))
% 0.85/1.07 (step t2.t86.t15.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t28.t22 t2.t86.t15.t28.t23))
% 0.85/1.07 (step t2.t86.t15.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t15.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t15.t28.t24 t2.t86.t15.t28.t25))
% 0.85/1.07 (step t2.t86.t15.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t15.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t15.t27 t2.t86.t15.t28))
% 0.85/1.07 (step t2.t86.t15.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t15.t26 t2.t86.t15.t29))
% 0.85/1.07 (step t2.t86.t15.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t15.t23 t2.t86.t15.t30 a4))
% 0.85/1.07 (step t2.t86.t15.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t15.t4 t2.t86.t15.t13 t2.t86.t15.t22 t2.t86.t15.t31 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t15.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t86.t15.t32))
% 0.85/1.07 (step t2.t86.t15.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t86.t15.t32))
% 0.85/1.07 (step t2.t86.t15.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t86.t15.t34 t2.t86.t15.t35))
% 0.85/1.07 (step t2.t86.t15.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t86.t15.t36 t2.t86.t15.t37))
% 0.85/1.07 (step t2.t86.t15.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t86.t15.t33 t2.t86.t15.t38))
% 0.85/1.07 (step t2.t86.t15.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t86.t15.t34 t2.t86.t15.t37))
% 0.85/1.07 (step t2.t86.t15.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t86.t15.t40 t2.t86.t15.t35))
% 0.85/1.07 (step t2.t86.t15.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t86.t15.t39 t2.t86.t15.t41))
% 0.85/1.07 (step t2.t86.t15.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t15.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t86.t15.t42 t2.t86.t15.t43))
% 0.85/1.07 (step t2.t86.t15 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t16 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t86.t14 t2.t86.t15))
% 0.85/1.07 (step t2.t86.t17 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t18 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t18.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t86.t18.t5 t2.t86.t18.t6))
% 0.85/1.07 (step t2.t86.t18.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t86.t18.t7 t2.t86.t18.t8))
% 0.85/1.07 (step t2.t86.t18.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t18.t4 t2.t86.t18.t9))
% 0.85/1.07 (step t2.t86.t18.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t18.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t18.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t86.t18.t12.t3))
% 0.85/1.07 (step t2.t86.t18.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t86.t18.t12.t4 t2.t86.t18.t12.t5))
% 0.85/1.07 (step t2.t86.t18.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t18.t12.t6))
% 0.85/1.07 (step t2.t86.t18.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t18.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t86.t18.t11 t2.t86.t18.t12))
% 0.85/1.07 (step t2.t86.t18.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t86.t18.t10 t2.t86.t18.t13))
% 0.85/1.07 (step t2.t86.t18.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t86.t18.t15 t2.t86.t18.t16))
% 0.85/1.07 (step t2.t86.t18.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t86.t18.t17 t2.t86.t18.t18))
% 0.85/1.07 (step t2.t86.t18.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t18.t14 t2.t86.t18.t19))
% 0.85/1.07 (step t2.t86.t18.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t18.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t18.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t86.t18.t22.t3))
% 0.85/1.07 (step t2.t86.t18.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t18.t22.t2 t2.t86.t18.t22.t4))
% 0.85/1.07 (step t2.t86.t18.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t86.t18.t22.t5))
% 0.85/1.07 (step t2.t86.t18.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t18.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t18.t21 t2.t86.t18.t22))
% 0.85/1.07 (step t2.t86.t18.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t18.t20 t2.t86.t18.t23))
% 0.85/1.07 (step t2.t86.t18.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t18.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t86.t18.t24 t2.t86.t18.t25))
% 0.85/1.07 (step t2.t86.t18.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t18.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t86.t18.t26 t2.t86.t18.t27))
% 0.85/1.07 (step t2.t86.t18 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t19 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t86.t17 t2.t86.t18))
% 0.85/1.07 (step t2.t86.t20 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t86.t16 t2.t86.t19))
% 0.85/1.07 (step t2.t86.t21 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t86.t13 t2.t86.t20 a7))
% 0.85/1.07 (step t2.t86.t22 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t23 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t24.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t24.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t24.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t24.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t24.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t24.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t24.t7.t7.t5))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t24.t7.t7.t6 t2.t86.t24.t7.t7.t8))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t24.t7.t7.t7 t2.t86.t24.t7.t7.t9))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t24.t7.t7.t6 t2.t86.t24.t7.t7.t11))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t24.t7.t7.t10 t2.t86.t24.t7.t7.t12))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t24.t7.t7.t6 t2.t86.t24.t7.t7.t13))
% 0.85/1.07 (step t2.t86.t24.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t7.t7.t14 t2.t86.t24.t7.t7.t15))
% 0.85/1.07 (step t2.t86.t24.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t24.t7.t6 t2.t86.t24.t7.t7))
% 0.85/1.07 (step t2.t86.t24.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t24.t7.t10.t5 t2.t86.t24.t7.t10.t6))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t24.t7.t10.t9.t3 t2.t86.t24.t7.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t7.t10.t8 t2.t86.t24.t7.t10.t9))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t7.t10.t7 t2.t86.t24.t7.t10.t10))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t24.t7.t10.t11 t2.t86.t24.t7.t10.t12))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t24.t7.t10.t15.t2 t2.t86.t24.t7.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t24.t7.t10.t14 t2.t86.t24.t7.t10.t15))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t24.t7.t10.t13 t2.t86.t24.t7.t10.t16))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t24.t7.t10.t4 t2.t86.t24.t7.t10.t17))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t24.t7.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t24.t7.t10.t19 t2.t86.t24.t7.t10.t20))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t24.t7.t10.t18 t2.t86.t24.t7.t10.t21))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t7.t10.t22 t2.t86.t24.t7.t10.t23))
% 0.85/1.07 (step t2.t86.t24.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t24.t7.t10.t24 t2.t86.t24.t7.t10.t25))
% 0.85/1.07 (step t2.t86.t24.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t24.t7.t9 t2.t86.t24.t7.t10))
% 0.85/1.07 (step t2.t86.t24.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t24.t7.t8 t2.t86.t24.t7.t11))
% 0.85/1.07 (step t2.t86.t24.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t24.t7.t5 t2.t86.t24.t7.t12 a4))
% 0.85/1.07 (step t2.t86.t24.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t24.t7.t4 t2.t86.t24.t7.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t24.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t24.t7.t14))
% 0.85/1.07 (step t2.t86.t24.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t24.t7.t14))
% 0.85/1.07 (step t2.t86.t24.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t24.t7.t16 t2.t86.t24.t7.t17))
% 0.85/1.07 (step t2.t86.t24.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t24.t7.t15 t2.t86.t24.t7.t18))
% 0.85/1.07 (step t2.t86.t24.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t24.t7.t19 t2.t86.t24.t7.t20))
% 0.85/1.07 (step t2.t86.t24.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t7.t21 t2.t86.t24.t7.t22))
% 0.85/1.07 (step t2.t86.t24.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t24.t6 t2.t86.t24.t7))
% 0.85/1.07 (step t2.t86.t24.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t24.t10.t4 t2.t86.t24.t10.t5))
% 0.85/1.07 (step t2.t86.t24.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t24.t10.t8.t3 t2.t86.t24.t10.t8.t4))
% 0.85/1.07 (step t2.t86.t24.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t10.t7 t2.t86.t24.t10.t8))
% 0.85/1.07 (step t2.t86.t24.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t10.t6 t2.t86.t24.t10.t9))
% 0.85/1.07 (step t2.t86.t24.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t24.t10.t10 t2.t86.t24.t10.t11))
% 0.85/1.07 (step t2.t86.t24.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t10.t12 t2.t86.t24.t10.t13))
% 0.85/1.07 (step t2.t86.t24.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t10.t14 t2.t86.t24.t10.t15))
% 0.85/1.07 (step t2.t86.t24.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t24.t10.t16 t2.t86.t24.t10.t17))
% 0.85/1.07 (step t2.t86.t24.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t24.t9 t2.t86.t24.t10))
% 0.85/1.07 (step t2.t86.t24.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t24.t8 t2.t86.t24.t11))
% 0.85/1.07 (step t2.t86.t24.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t24.t5 t2.t86.t24.t12 a5))
% 0.85/1.07 (step t2.t86.t24.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t24.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t24.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t24.t16.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t24.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t24.t16.t5))
% 0.85/1.07 (step t2.t86.t24.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t24.t16.t5))
% 0.85/1.07 (step t2.t86.t24.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t24.t16.t6 t2.t86.t24.t16.t8))
% 0.85/1.07 (step t2.t86.t24.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t24.t16.t7 t2.t86.t24.t16.t9))
% 0.85/1.07 (step t2.t86.t24.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t24.t16.t6 t2.t86.t24.t16.t11))
% 0.85/1.07 (step t2.t86.t24.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t24.t16.t10 t2.t86.t24.t16.t12))
% 0.85/1.07 (step t2.t86.t24.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t24.t16.t6 t2.t86.t24.t16.t13))
% 0.85/1.07 (step t2.t86.t24.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t16.t14 t2.t86.t24.t16.t15))
% 0.85/1.07 (step t2.t86.t24.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t24.t15 t2.t86.t24.t16))
% 0.85/1.07 (step t2.t86.t24.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t24.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t24.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t24.t19.t5 t2.t86.t24.t19.t6))
% 0.85/1.07 (step t2.t86.t24.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t24.t19.t9.t3 t2.t86.t24.t19.t9.t4))
% 0.85/1.07 (step t2.t86.t24.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t19.t8 t2.t86.t24.t19.t9))
% 0.85/1.07 (step t2.t86.t24.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t24.t19.t7 t2.t86.t24.t19.t10))
% 0.85/1.07 (step t2.t86.t24.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t24.t19.t11 t2.t86.t24.t19.t12))
% 0.85/1.07 (step t2.t86.t24.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t24.t19.t15.t2 t2.t86.t24.t19.t15.t3))
% 0.85/1.07 (step t2.t86.t24.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t24.t19.t14 t2.t86.t24.t19.t15))
% 0.85/1.07 (step t2.t86.t24.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t24.t19.t13 t2.t86.t24.t19.t16))
% 0.85/1.07 (step t2.t86.t24.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t24.t19.t4 t2.t86.t24.t19.t17))
% 0.85/1.07 (step t2.t86.t24.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t24.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t24.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t24.t19.t20.t2))
% 0.85/1.07 (step t2.t86.t24.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t24.t19.t19 t2.t86.t24.t19.t20))
% 0.85/1.07 (step t2.t86.t24.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t24.t19.t18 t2.t86.t24.t19.t21))
% 0.85/1.07 (step t2.t86.t24.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t19.t22 t2.t86.t24.t19.t23))
% 0.85/1.07 (step t2.t86.t24.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t24.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t24.t19.t24 t2.t86.t24.t19.t25))
% 0.85/1.07 (step t2.t86.t24.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t24.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t24.t18 t2.t86.t24.t19))
% 0.85/1.07 (step t2.t86.t24.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t24.t17 t2.t86.t24.t20))
% 0.85/1.07 (step t2.t86.t24.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t24.t14 t2.t86.t24.t21 a4))
% 0.85/1.07 (step t2.t86.t24.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t24.t4 t2.t86.t24.t13 t2.t86.t24.t22 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t24.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t24.t23))
% 0.85/1.07 (step t2.t86.t24.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t24.t23))
% 0.85/1.07 (step t2.t86.t24.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t24.t25 t2.t86.t24.t26))
% 0.85/1.07 (step t2.t86.t24.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t24.t24 t2.t86.t24.t27))
% 0.85/1.07 (step t2.t86.t24.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t86.t24.t28 t2.t86.t24.t29))
% 0.85/1.07 (step t2.t86.t24.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t24.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t86.t24.t30 t2.t86.t24.t31))
% 0.85/1.07 (step t2.t86.t24 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t25 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t86.t23 t2.t86.t24))
% 0.85/1.07 (step t2.t86.t26 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t27 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t27.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t27.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t27.t4 t2.t86.t27.t5))
% 0.85/1.07 (step t2.t86.t27.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t27.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t27.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t27.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t27.t8.t3 t2.t86.t27.t8.t4))
% 0.85/1.07 (step t2.t86.t27.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t27.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t27.t7 t2.t86.t27.t8))
% 0.85/1.07 (step t2.t86.t27.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t27.t6 t2.t86.t27.t9))
% 0.85/1.07 (step t2.t86.t27.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t86.t27.t10 t2.t86.t27.t11))
% 0.85/1.07 (step t2.t86.t27.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t27.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t86.t27.t12 t2.t86.t27.t13))
% 0.85/1.07 (step t2.t86.t27.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t27.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t27.t14 t2.t86.t27.t15))
% 0.85/1.07 (step t2.t86.t27.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t27.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t86.t27.t16 t2.t86.t27.t17))
% 0.85/1.07 (step t2.t86.t27 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t28 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t86.t26 t2.t86.t27))
% 0.85/1.07 (step t2.t86.t29 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t86.t25 t2.t86.t28))
% 0.85/1.07 (step t2.t86.t30 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t86.t22 t2.t86.t29 a6))
% 0.85/1.07 (step t2.t86.t31 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t32 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t33 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t33.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t33.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t33.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t33.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t33.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t33.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t33.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t33.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t33.t7.t5))
% 0.85/1.07 (step t2.t86.t33.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t33.t7.t5))
% 0.85/1.07 (step t2.t86.t33.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t33.t7.t6 t2.t86.t33.t7.t8))
% 0.85/1.07 (step t2.t86.t33.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t33.t7.t7 t2.t86.t33.t7.t9))
% 0.85/1.07 (step t2.t86.t33.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t33.t7.t6 t2.t86.t33.t7.t11))
% 0.85/1.07 (step t2.t86.t33.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t33.t7.t10 t2.t86.t33.t7.t12))
% 0.85/1.07 (step t2.t86.t33.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t33.t7.t6 t2.t86.t33.t7.t13))
% 0.85/1.07 (step t2.t86.t33.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t33.t7.t14 t2.t86.t33.t7.t15))
% 0.85/1.07 (step t2.t86.t33.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t33.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t33.t6 t2.t86.t33.t7))
% 0.85/1.07 (step t2.t86.t33.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t33.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t33.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t33.t10.t5 t2.t86.t33.t10.t6))
% 0.85/1.07 (step t2.t86.t33.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t33.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t33.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t33.t10.t9.t3 t2.t86.t33.t10.t9.t4))
% 0.85/1.07 (step t2.t86.t33.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t33.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t33.t10.t8 t2.t86.t33.t10.t9))
% 0.85/1.07 (step t2.t86.t33.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t33.t10.t7 t2.t86.t33.t10.t10))
% 0.85/1.07 (step t2.t86.t33.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t33.t10.t11 t2.t86.t33.t10.t12))
% 0.85/1.07 (step t2.t86.t33.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t33.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t33.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t33.t10.t15.t2 t2.t86.t33.t10.t15.t3))
% 0.85/1.07 (step t2.t86.t33.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t33.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t33.t10.t14 t2.t86.t33.t10.t15))
% 0.85/1.07 (step t2.t86.t33.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t33.t10.t13 t2.t86.t33.t10.t16))
% 0.85/1.07 (step t2.t86.t33.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t33.t10.t4 t2.t86.t33.t10.t17))
% 0.85/1.07 (step t2.t86.t33.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t33.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t33.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t33.t10.t20.t2))
% 0.85/1.07 (step t2.t86.t33.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t33.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t33.t10.t19 t2.t86.t33.t10.t20))
% 0.85/1.07 (step t2.t86.t33.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t33.t10.t18 t2.t86.t33.t10.t21))
% 0.85/1.07 (step t2.t86.t33.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t33.t10.t22 t2.t86.t33.t10.t23))
% 0.85/1.07 (step t2.t86.t33.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t33.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t33.t10.t24 t2.t86.t33.t10.t25))
% 0.85/1.07 (step t2.t86.t33.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t33.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t33.t9 t2.t86.t33.t10))
% 0.85/1.07 (step t2.t86.t33.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t33.t8 t2.t86.t33.t11))
% 0.85/1.07 (step t2.t86.t33.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t33.t5 t2.t86.t33.t12 a4))
% 0.85/1.07 (step t2.t86.t33.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t33.t4 t2.t86.t33.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t33.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t33.t14))
% 0.85/1.07 (step t2.t86.t33.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t33.t14))
% 0.85/1.07 (step t2.t86.t33.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t33.t16 t2.t86.t33.t17))
% 0.85/1.07 (step t2.t86.t33.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t33.t15 t2.t86.t33.t18))
% 0.85/1.07 (step t2.t86.t33.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t86.t33.t19 t2.t86.t33.t20))
% 0.85/1.07 (step t2.t86.t33.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t33.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t86.t33.t21 t2.t86.t33.t22))
% 0.85/1.07 (step t2.t86.t33 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t34 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t86.t32 t2.t86.t33))
% 0.85/1.07 (step t2.t86.t35 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t36 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t36.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t36.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t36.t4 t2.t86.t36.t5))
% 0.85/1.07 (step t2.t86.t36.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t36.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t36.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t36.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t36.t8.t3 t2.t86.t36.t8.t4))
% 0.85/1.07 (step t2.t86.t36.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t36.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t36.t7 t2.t86.t36.t8))
% 0.85/1.07 (step t2.t86.t36.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t36.t6 t2.t86.t36.t9))
% 0.85/1.07 (step t2.t86.t36.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t86.t36.t10 t2.t86.t36.t11))
% 0.85/1.07 (step t2.t86.t36.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t36.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t36.t12 t2.t86.t36.t13))
% 0.85/1.07 (step t2.t86.t36.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t36.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t86.t36.t14 t2.t86.t36.t15))
% 0.85/1.07 (step t2.t86.t36.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t36.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t86.t36.t16 t2.t86.t36.t17))
% 0.85/1.07 (step t2.t86.t36 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t86.t37 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t86.t35 t2.t86.t36))
% 0.85/1.07 (step t2.t86.t38 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t34 t2.t86.t37))
% 0.85/1.07 (step t2.t86.t39 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t86.t31 t2.t86.t38 a5))
% 0.85/1.07 (step t2.t86.t40 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t86.t41 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t42 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t42.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t86.t42.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t42.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t42.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t42.t5))
% 0.85/1.07 (step t2.t86.t42.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t86.t42.t5))
% 0.85/1.07 (step t2.t86.t42.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t86.t42.t6 t2.t86.t42.t8))
% 0.85/1.07 (step t2.t86.t42.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t86.t42.t7 t2.t86.t42.t9))
% 0.85/1.07 (step t2.t86.t42.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t86.t42.t6 t2.t86.t42.t11))
% 0.85/1.07 (step t2.t86.t42.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t86.t42.t10 t2.t86.t42.t12))
% 0.85/1.07 (step t2.t86.t42.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t86.t42.t6 t2.t86.t42.t13))
% 0.85/1.07 (step t2.t86.t42.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t42.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t86.t42.t14 t2.t86.t42.t15))
% 0.85/1.07 (step t2.t86.t42 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t43 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t86.t41 t2.t86.t42))
% 0.85/1.07 (step t2.t86.t44 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t86.t45 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t45.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t86.t45.t5 t2.t86.t45.t6))
% 0.85/1.07 (step t2.t86.t45.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t45.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t45.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t86.t45.t9.t3 t2.t86.t45.t9.t4))
% 0.85/1.07 (step t2.t86.t45.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t86.t45.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t45.t8 t2.t86.t45.t9))
% 0.85/1.07 (step t2.t86.t45.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t86.t45.t7 t2.t86.t45.t10))
% 0.85/1.07 (step t2.t86.t45.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t45.t11 t2.t86.t45.t12))
% 0.85/1.07 (step t2.t86.t45.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t45.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t45.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t86.t45.t15.t2 t2.t86.t45.t15.t3))
% 0.85/1.07 (step t2.t86.t45.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t86.t45.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t45.t14 t2.t86.t45.t15))
% 0.85/1.07 (step t2.t86.t45.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t86.t45.t13 t2.t86.t45.t16))
% 0.85/1.07 (step t2.t86.t45.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t86.t45.t4 t2.t86.t45.t17))
% 0.85/1.07 (step t2.t86.t45.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t86.t45.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t86.t45.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t86.t45.t20.t2))
% 0.85/1.07 (step t2.t86.t45.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t45.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t45.t19 t2.t86.t45.t20))
% 0.85/1.07 (step t2.t86.t45.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t86.t45.t18 t2.t86.t45.t21))
% 0.85/1.07 (step t2.t86.t45.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t45.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t86.t45.t22 t2.t86.t45.t23))
% 0.85/1.07 (step t2.t86.t45.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t86.t45.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t86.t45.t24 t2.t86.t45.t25))
% 0.85/1.07 (step t2.t86.t45 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t86.t46 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t86.t44 t2.t86.t45))
% 0.85/1.07 (step t2.t86.t47 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t86.t43 t2.t86.t46))
% 0.85/1.07 (step t2.t86.t48 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t86.t40 t2.t86.t47 a4))
% 0.85/1.07 (step t2.t86.t49 (cl (and (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t86.t3 a10 a9 t2.t86.t12 t2.t86.t21 t2.t86.t30 t2.t86.t39 t2.t86.t48 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t86.t50 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t86.t49))
% 0.85/1.07 (step t2.t86.t51 (cl (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule and :premises (t2.t86.t49))
% 0.85/1.07 (anchor :step t2.t86.t52 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t86.t52.t1 (cl (= X X)) :rule refl)
% 0.85/1.07 (step t2.t86.t52.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t52.t3 (cl (= (@ Phi X) (@ Phi X))) :rule refl)
% 0.85/1.07 (step t2.t86.t52.t4 (cl (= (@ tptp.mnot (@ Phi X)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)))) :rule cong :premises (t2.t86.t50 t2.t86.t52.t3))
% 0.85/1.07 (step t2.t86.t52.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t52.t6 (cl (= (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) :rule cong :premises (t2.t86.t52.t4 t2.t86.t52.t5))
% 0.85/1.07 (step t2.t86.t52 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t86.t53 (cl (= (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))))) :rule cong :premises (t2.t86.t51 t2.t86.t52))
% 0.85/1.07 (step t2.t86.t54 (cl (= (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))))) :rule cong :premises (t2.t86.t50 t2.t86.t53))
% 0.85/1.07 (step t2.t86.t55 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t86.t56 (cl (= (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) :rule cong :premises (t2.t86.t54 t2.t86.t55))
% 0.85/1.07 (step t2.t86 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t87 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) :rule cong :premises (t2.t85 t2.t86))
% 0.85/1.07 (step t2.t88 (cl (= tptp.mexists_ind tptp.mexists_ind)) :rule refl)
% 0.85/1.07 (anchor :step t2.t89 :args ((Phi (-> tptp.mu $$unsorted Bool)) (:= Phi Phi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t89.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t89.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t89.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t89.t4 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))))) :rule refl)
% 0.85/1.07 (anchor :step t2.t89.t5 :args ((X tptp.mu) (:= X X) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t89.t5.t1 (cl (= X X)) :rule refl)
% 0.85/1.07 (step t2.t89.t5.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t89.t5.t3 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t5.t4 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t89.t5.t5 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0))) :rule cong :premises (t2.t89.t5.t3 t2.t89.t5.t4))
% 0.85/1.07 (step t2.t89.t5.t6 (cl (= (@ (lambda ((W $$unsorted)) (not (@ (@ Phi X) W))) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t5.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0) (not (@ (@ Phi X) __flatten_var_0)))) :rule trans :premises (t2.t89.t5.t5 t2.t89.t5.t6))
% 0.85/1.07 (step t2.t89.t5 (cl (= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t89.t6 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule cong :premises (t2.t89.t4 t2.t89.t5))
% 0.85/1.07 (step t2.t89.t7 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t89.t8 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t89.t8.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (anchor :step t2.t89.t8.t2 :args ((X tptp.mu) (:= X X)))
% 0.85/1.07 (step t2.t89.t8.t2.t1 (cl (= X X)) :rule refl)
% 0.85/1.07 (step t2.t89.t8.t2.t2 (cl (= (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t8.t2.t3 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t89.t8.t2.t4 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W))) :rule cong :premises (t2.t89.t8.t2.t2 t2.t89.t8.t2.t3))
% 0.85/1.07 (step t2.t89.t8.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) W) (not (@ (@ Phi X) W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t8.t2.t6 (cl (= (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W) (not (@ (@ Phi X) W)))) :rule trans :premises (t2.t89.t8.t2.t4 t2.t89.t8.t2.t5))
% 0.85/1.07 (step t2.t89.t8.t2 (cl (= (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule bind)
% 0.85/1.07 (step t2.t89.t8 (cl (= (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0))) X) W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule bind)
% 0.85/1.07 (step t2.t89.t9 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (not (@ (@ Phi X) __flatten_var_0)))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t89.t7 t2.t89.t8))
% 0.85/1.07 (step t2.t89.t10 (cl (= (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule trans :premises (t2.t89.t6 t2.t89.t9))
% 0.85/1.07 (step t2.t89.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule cong :premises (t2.t89.t3 t2.t89.t10))
% 0.85/1.07 (step t2.t89.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t89.t13 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t89.t13.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t89.t13.t2 (cl (= (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t13.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))))) :rule cong :premises (t2.t89.t13.t2))
% 0.85/1.07 (step t2.t89.t13 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W)))) W))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule bind)
% 0.85/1.07 (step t2.t89.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t89.t12 t2.t89.t13))
% 0.85/1.07 (step t2.t89.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))))) :rule trans :premises (t2.t89.t11 t2.t89.t14))
% 0.85/1.07 (step t2.t89.t16 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t89.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0))) :rule cong :premises (t2.t89.t15 t2.t89.t16))
% 0.85/1.07 (step t2.t89.t18 (cl (= (@ (lambda ((W $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) W))))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t89.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) :rule trans :premises (t2.t89.t17 t2.t89.t18))
% 0.85/1.07 (step t2.t89 (cl (= (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0)) (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t90 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W))) (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule cong :premises (t2.t88 t2.t89))
% 0.85/1.07 (step t2.t91 (cl (= (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))))) :rule trans :premises (t2.t87 t2.t90))
% 0.85/1.07 (step t2.t92 (cl (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0))))))) :rule resolution :premises (t2.t84 t2.t91 a11))
% 0.85/1.07 (step t2.t93 (cl (not (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t94 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t4 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t5 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t6 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t7.t7.t7.t5))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t7.t7.t7.t5))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t6 t2.t95.t7.t7.t7.t7.t8))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t7 t2.t95.t7.t7.t7.t7.t9))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t6 t2.t95.t7.t7.t7.t7.t11))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t10 t2.t95.t7.t7.t7.t7.t12))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t6 t2.t95.t7.t7.t7.t7.t13))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t7.t7.t14 t2.t95.t7.t7.t7.t7.t15))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t7.t7.t6 t2.t95.t7.t7.t7.t7))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t5 t2.t95.t7.t7.t7.t10.t6))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t9.t3 t2.t95.t7.t7.t7.t10.t9.t4))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t8 t2.t95.t7.t7.t7.t10.t9))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t7 t2.t95.t7.t7.t7.t10.t10))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t11 t2.t95.t7.t7.t7.t10.t12))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t15.t2 t2.t95.t7.t7.t7.t10.t15.t3))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t14 t2.t95.t7.t7.t7.t10.t15))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t13 t2.t95.t7.t7.t7.t10.t16))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t4 t2.t95.t7.t7.t7.t10.t17))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t20.t2))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t19 t2.t95.t7.t7.t7.t10.t20))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t18 t2.t95.t7.t7.t7.t10.t21))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t7.t10.t22 t2.t95.t7.t7.t7.t10.t23))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t7.t7.t10.t24 t2.t95.t7.t7.t7.t10.t25))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t7.t7.t7.t9 t2.t95.t7.t7.t7.t10))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t7.t7.t7.t8 t2.t95.t7.t7.t7.t11))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t7.t7.t7.t5 t2.t95.t7.t7.t7.t12 a4))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t7.t7.t4 t2.t95.t7.t7.t7.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t7.t7.t14))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t7.t7.t14))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t7.t7.t16 t2.t95.t7.t7.t7.t17))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t7.t7.t15 t2.t95.t7.t7.t7.t18))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t95.t7.t7.t7.t19 t2.t95.t7.t7.t7.t20))
% 0.85/1.07 (step t2.t95.t7.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t7.t21 t2.t95.t7.t7.t7.t22))
% 0.85/1.07 (step t2.t95.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t7.t6 t2.t95.t7.t7.t7))
% 0.85/1.07 (step t2.t95.t7.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t7.t10.t4 t2.t95.t7.t7.t10.t5))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t7.t10.t8.t3 t2.t95.t7.t7.t10.t8.t4))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t10.t7 t2.t95.t7.t7.t10.t8))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t10.t6 t2.t95.t7.t7.t10.t9))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t95.t7.t7.t10.t10 t2.t95.t7.t7.t10.t11))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t10.t12 t2.t95.t7.t7.t10.t13))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t10.t14 t2.t95.t7.t7.t10.t15))
% 0.85/1.07 (step t2.t95.t7.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t95.t7.t7.t10.t16 t2.t95.t7.t7.t10.t17))
% 0.85/1.07 (step t2.t95.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t7.t7.t9 t2.t95.t7.t7.t10))
% 0.85/1.07 (step t2.t95.t7.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t7.t8 t2.t95.t7.t7.t11))
% 0.85/1.07 (step t2.t95.t7.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t95.t7.t7.t5 t2.t95.t7.t7.t12 a5))
% 0.85/1.07 (step t2.t95.t7.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t7.t16.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t7.t16.t5))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t7.t16.t5))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t7.t16.t6 t2.t95.t7.t7.t16.t8))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t7.t16.t7 t2.t95.t7.t7.t16.t9))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t7.t7.t16.t6 t2.t95.t7.t7.t16.t11))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t7.t7.t16.t10 t2.t95.t7.t7.t16.t12))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t7.t7.t16.t6 t2.t95.t7.t7.t16.t13))
% 0.85/1.07 (step t2.t95.t7.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t16.t14 t2.t95.t7.t7.t16.t15))
% 0.85/1.07 (step t2.t95.t7.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t7.t15 t2.t95.t7.t7.t16))
% 0.85/1.07 (step t2.t95.t7.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t7.t19.t5 t2.t95.t7.t7.t19.t6))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t7.t19.t9.t3 t2.t95.t7.t7.t19.t9.t4))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t19.t8 t2.t95.t7.t7.t19.t9))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t7.t19.t7 t2.t95.t7.t7.t19.t10))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t7.t19.t11 t2.t95.t7.t7.t19.t12))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t7.t7.t19.t15.t2 t2.t95.t7.t7.t19.t15.t3))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t7.t19.t14 t2.t95.t7.t7.t19.t15))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t7.t19.t13 t2.t95.t7.t7.t19.t16))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t7.t7.t19.t4 t2.t95.t7.t7.t19.t17))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t7.t19.t20.t2))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t7.t19.t19 t2.t95.t7.t7.t19.t20))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t7.t19.t18 t2.t95.t7.t7.t19.t21))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t19.t22 t2.t95.t7.t7.t19.t23))
% 0.85/1.07 (step t2.t95.t7.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t7.t19.t24 t2.t95.t7.t7.t19.t25))
% 0.85/1.07 (step t2.t95.t7.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t7.t7.t18 t2.t95.t7.t7.t19))
% 0.85/1.07 (step t2.t95.t7.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t7.t7.t17 t2.t95.t7.t7.t20))
% 0.85/1.07 (step t2.t95.t7.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t7.t7.t14 t2.t95.t7.t7.t21 a4))
% 0.85/1.07 (step t2.t95.t7.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t7.t4 t2.t95.t7.t7.t13 t2.t95.t7.t7.t22 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t7.t23))
% 0.85/1.07 (step t2.t95.t7.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t7.t23))
% 0.85/1.07 (step t2.t95.t7.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t7.t7.t25 t2.t95.t7.t7.t26))
% 0.85/1.07 (step t2.t95.t7.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t7.t7.t24 t2.t95.t7.t7.t27))
% 0.85/1.07 (step t2.t95.t7.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t95.t7.t7.t28 t2.t95.t7.t7.t29))
% 0.85/1.07 (step t2.t95.t7.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t7.t30 t2.t95.t7.t7.t31))
% 0.85/1.07 (step t2.t95.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t6 t2.t95.t7.t7))
% 0.85/1.07 (step t2.t95.t7.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t10.t4 t2.t95.t7.t10.t5))
% 0.85/1.07 (step t2.t95.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t10.t8.t3 t2.t95.t7.t10.t8.t4))
% 0.85/1.07 (step t2.t95.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t10.t7 t2.t95.t7.t10.t8))
% 0.85/1.07 (step t2.t95.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t10.t6 t2.t95.t7.t10.t9))
% 0.85/1.07 (step t2.t95.t7.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t95.t7.t10.t10 t2.t95.t7.t10.t11))
% 0.85/1.07 (step t2.t95.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t95.t7.t10.t12 t2.t95.t7.t10.t13))
% 0.85/1.07 (step t2.t95.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t10.t14 t2.t95.t7.t10.t15))
% 0.85/1.07 (step t2.t95.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t95.t7.t10.t16 t2.t95.t7.t10.t17))
% 0.85/1.07 (step t2.t95.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t95.t7.t9 t2.t95.t7.t10))
% 0.85/1.07 (step t2.t95.t7.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t8 t2.t95.t7.t11))
% 0.85/1.07 (step t2.t95.t7.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t95.t7.t5 t2.t95.t7.t12 a6))
% 0.85/1.07 (step t2.t95.t7.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t16.t7.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t16.t7.t5))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t16.t7.t5))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t16.t7.t6 t2.t95.t7.t16.t7.t8))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t16.t7.t7 t2.t95.t7.t16.t7.t9))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t7.t16.t7.t6 t2.t95.t7.t16.t7.t11))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t7.t16.t7.t10 t2.t95.t7.t16.t7.t12))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t7.t16.t7.t6 t2.t95.t7.t16.t7.t13))
% 0.85/1.07 (step t2.t95.t7.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t16.t7.t14 t2.t95.t7.t16.t7.t15))
% 0.85/1.07 (step t2.t95.t7.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t16.t6 t2.t95.t7.t16.t7))
% 0.85/1.07 (step t2.t95.t7.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t16.t10.t5 t2.t95.t7.t16.t10.t6))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t16.t10.t9.t3 t2.t95.t7.t16.t10.t9.t4))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t16.t10.t8 t2.t95.t7.t16.t10.t9))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t16.t10.t7 t2.t95.t7.t16.t10.t10))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t16.t10.t11 t2.t95.t7.t16.t10.t12))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t7.t16.t10.t15.t2 t2.t95.t7.t16.t10.t15.t3))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t16.t10.t14 t2.t95.t7.t16.t10.t15))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t16.t10.t13 t2.t95.t7.t16.t10.t16))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t7.t16.t10.t4 t2.t95.t7.t16.t10.t17))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t16.t10.t20.t2))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t16.t10.t19 t2.t95.t7.t16.t10.t20))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t16.t10.t18 t2.t95.t7.t16.t10.t21))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t16.t10.t22 t2.t95.t7.t16.t10.t23))
% 0.85/1.07 (step t2.t95.t7.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t16.t10.t24 t2.t95.t7.t16.t10.t25))
% 0.85/1.07 (step t2.t95.t7.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t7.t16.t9 t2.t95.t7.t16.t10))
% 0.85/1.07 (step t2.t95.t7.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t7.t16.t8 t2.t95.t7.t16.t11))
% 0.85/1.07 (step t2.t95.t7.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t7.t16.t5 t2.t95.t7.t16.t12 a4))
% 0.85/1.07 (step t2.t95.t7.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t16.t4 t2.t95.t7.t16.t13 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t16.t14))
% 0.85/1.07 (step t2.t95.t7.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t16.t14))
% 0.85/1.07 (step t2.t95.t7.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t16.t16 t2.t95.t7.t16.t17))
% 0.85/1.07 (step t2.t95.t7.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t16.t15 t2.t95.t7.t16.t18))
% 0.85/1.07 (step t2.t95.t7.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t95.t7.t16.t19 t2.t95.t7.t16.t20))
% 0.85/1.07 (step t2.t95.t7.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t16.t21 t2.t95.t7.t16.t22))
% 0.85/1.07 (step t2.t95.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t15 t2.t95.t7.t16))
% 0.85/1.07 (step t2.t95.t7.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t19.t4 t2.t95.t7.t19.t5))
% 0.85/1.07 (step t2.t95.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t19.t8.t3 t2.t95.t7.t19.t8.t4))
% 0.85/1.07 (step t2.t95.t7.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t19.t7 t2.t95.t7.t19.t8))
% 0.85/1.07 (step t2.t95.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t19.t6 t2.t95.t7.t19.t9))
% 0.85/1.07 (step t2.t95.t7.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t95.t7.t19.t10 t2.t95.t7.t19.t11))
% 0.85/1.07 (step t2.t95.t7.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t19.t12 t2.t95.t7.t19.t13))
% 0.85/1.07 (step t2.t95.t7.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t19.t14 t2.t95.t7.t19.t15))
% 0.85/1.07 (step t2.t95.t7.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t95.t7.t19.t16 t2.t95.t7.t19.t17))
% 0.85/1.07 (step t2.t95.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t7.t18 t2.t95.t7.t19))
% 0.85/1.07 (step t2.t95.t7.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t17 t2.t95.t7.t20))
% 0.85/1.07 (step t2.t95.t7.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t95.t7.t14 t2.t95.t7.t21 a5))
% 0.85/1.07 (step t2.t95.t7.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.07 (step t2.t95.t7.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.07 (step t2.t95.t7.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t25.t4 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t7.t25.t5))
% 0.85/1.07 (step t2.t95.t7.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t7.t25.t5))
% 0.85/1.07 (step t2.t95.t7.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t7.t25.t6 t2.t95.t7.t25.t8))
% 0.85/1.07 (step t2.t95.t7.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t7.t25.t7 t2.t95.t7.t25.t9))
% 0.85/1.07 (step t2.t95.t7.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t7.t25.t6 t2.t95.t7.t25.t11))
% 0.85/1.07 (step t2.t95.t7.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t7.t25.t10 t2.t95.t7.t25.t12))
% 0.85/1.07 (step t2.t95.t7.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t7.t25.t6 t2.t95.t7.t25.t13))
% 0.85/1.07 (step t2.t95.t7.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t25.t14 t2.t95.t7.t25.t15))
% 0.85/1.07 (step t2.t95.t7.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t7.t24 t2.t95.t7.t25))
% 0.85/1.07 (step t2.t95.t7.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t7.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t7.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t7.t28.t5 t2.t95.t7.t28.t6))
% 0.85/1.07 (step t2.t95.t7.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t7.t28.t9.t3 t2.t95.t7.t28.t9.t4))
% 0.85/1.07 (step t2.t95.t7.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t28.t8 t2.t95.t7.t28.t9))
% 0.85/1.07 (step t2.t95.t7.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t7.t28.t7 t2.t95.t7.t28.t10))
% 0.85/1.07 (step t2.t95.t7.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t28.t11 t2.t95.t7.t28.t12))
% 0.85/1.07 (step t2.t95.t7.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t7.t28.t15.t2 t2.t95.t7.t28.t15.t3))
% 0.85/1.07 (step t2.t95.t7.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t28.t14 t2.t95.t7.t28.t15))
% 0.85/1.07 (step t2.t95.t7.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t7.t28.t13 t2.t95.t7.t28.t16))
% 0.85/1.07 (step t2.t95.t7.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t7.t28.t4 t2.t95.t7.t28.t17))
% 0.85/1.07 (step t2.t95.t7.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t7.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.07 (step t2.t95.t7.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t7.t28.t20.t2))
% 0.85/1.07 (step t2.t95.t7.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t28.t19 t2.t95.t7.t28.t20))
% 0.85/1.07 (step t2.t95.t7.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t7.t28.t18 t2.t95.t7.t28.t21))
% 0.85/1.07 (step t2.t95.t7.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t28.t22 t2.t95.t7.t28.t23))
% 0.85/1.07 (step t2.t95.t7.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t7.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t7.t28.t24 t2.t95.t7.t28.t25))
% 0.85/1.07 (step t2.t95.t7.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t7.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t7.t27 t2.t95.t7.t28))
% 0.85/1.07 (step t2.t95.t7.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t7.t26 t2.t95.t7.t29))
% 0.85/1.07 (step t2.t95.t7.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t7.t23 t2.t95.t7.t30 a4))
% 0.85/1.07 (step t2.t95.t7.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t7.t4 t2.t95.t7.t13 t2.t95.t7.t22 t2.t95.t7.t31 a3 a2 a1 a0))
% 0.85/1.07 (step t2.t95.t7.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t95.t7.t32))
% 0.85/1.07 (step t2.t95.t7.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t95.t7.t32))
% 0.85/1.07 (step t2.t95.t7.t35 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t95.t7.t34 t2.t95.t7.t35))
% 0.85/1.07 (step t2.t95.t7.t37 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t95.t7.t36 t2.t95.t7.t37))
% 0.85/1.07 (step t2.t95.t7.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t95.t7.t33 t2.t95.t7.t38))
% 0.85/1.07 (step t2.t95.t7.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t95.t7.t34 t2.t95.t7.t37))
% 0.85/1.07 (step t2.t95.t7.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t95.t7.t40 t2.t95.t7.t35))
% 0.85/1.07 (step t2.t95.t7.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t95.t7.t39 t2.t95.t7.t41))
% 0.85/1.07 (step t2.t95.t7.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t7.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t95.t7.t42 t2.t95.t7.t43))
% 0.85/1.07 (step t2.t95.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.85/1.07 (step t2.t95.t8 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t95.t6 t2.t95.t7))
% 0.85/1.07 (step t2.t95.t9 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.85/1.07 (anchor :step t2.t95.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t6 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t95.t10.t5 t2.t95.t10.t6))
% 0.85/1.07 (step t2.t95.t10.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t95.t10.t7 t2.t95.t10.t8))
% 0.85/1.07 (step t2.t95.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t10.t4 t2.t95.t10.t9))
% 0.85/1.07 (step t2.t95.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t10.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t10.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t95.t10.t12.t3))
% 0.85/1.07 (step t2.t95.t10.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t95.t10.t12.t4 t2.t95.t10.t12.t5))
% 0.85/1.07 (step t2.t95.t10.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t10.t12.t6))
% 0.85/1.07 (step t2.t95.t10.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t10.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t95.t10.t11 t2.t95.t10.t12))
% 0.85/1.07 (step t2.t95.t10.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t95.t10.t10 t2.t95.t10.t13))
% 0.85/1.07 (step t2.t95.t10.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t16 (cl (= Phi Phi)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t95.t10.t15 t2.t95.t10.t16))
% 0.85/1.07 (step t2.t95.t10.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t95.t10.t17 t2.t95.t10.t18))
% 0.85/1.07 (step t2.t95.t10.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t95.t10.t14 t2.t95.t10.t19))
% 0.85/1.07 (step t2.t95.t10.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (anchor :step t2.t95.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.07 (step t2.t95.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t95.t10.t22.t3))
% 0.85/1.07 (step t2.t95.t10.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t95.t10.t22.t2 t2.t95.t10.t22.t4))
% 0.85/1.07 (step t2.t95.t10.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t95.t10.t22.t5))
% 0.85/1.07 (step t2.t95.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t10.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t10.t21 t2.t95.t10.t22))
% 0.85/1.07 (step t2.t95.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t10.t20 t2.t95.t10.t23))
% 0.85/1.07 (step t2.t95.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.07 (step t2.t95.t10.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t95.t10.t24 t2.t95.t10.t25))
% 0.85/1.07 (step t2.t95.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.85/1.07 (step t2.t95.t10.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t95.t10.t26 t2.t95.t10.t27))
% 0.85/1.07 (step t2.t95.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.85/1.07 (step t2.t95.t11 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t95.t9 t2.t95.t10))
% 0.85/1.07 (step t2.t95.t12 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t95.t8 t2.t95.t11))
% 0.85/1.07 (step t2.t95.t13 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t95.t5 t2.t95.t12 a7))
% 0.85/1.07 (step t2.t95.t14 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t15 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t16.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t16.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t16.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t16.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t16.t7.t7.t4 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t16.t7.t7.t5))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t16.t7.t7.t5))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t16.t7.t7.t6 t2.t95.t16.t7.t7.t8))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t16.t7.t7.t7 t2.t95.t16.t7.t7.t9))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t16.t7.t7.t6 t2.t95.t16.t7.t7.t11))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t16.t7.t7.t10 t2.t95.t16.t7.t7.t12))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t16.t7.t7.t6 t2.t95.t16.t7.t7.t13))
% 0.85/1.08 (step t2.t95.t16.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t7.t7.t14 t2.t95.t16.t7.t7.t15))
% 0.85/1.08 (step t2.t95.t16.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t16.t7.t6 t2.t95.t16.t7.t7))
% 0.85/1.08 (step t2.t95.t16.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t16.t7.t10.t5 t2.t95.t16.t7.t10.t6))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t16.t7.t10.t9.t3 t2.t95.t16.t7.t10.t9.t4))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t7.t10.t8 t2.t95.t16.t7.t10.t9))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t7.t10.t7 t2.t95.t16.t7.t10.t10))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t16.t7.t10.t11 t2.t95.t16.t7.t10.t12))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t16.t7.t10.t15.t2 t2.t95.t16.t7.t10.t15.t3))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t16.t7.t10.t14 t2.t95.t16.t7.t10.t15))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t16.t7.t10.t13 t2.t95.t16.t7.t10.t16))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t16.t7.t10.t4 t2.t95.t16.t7.t10.t17))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t16.t7.t10.t20.t2))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t16.t7.t10.t19 t2.t95.t16.t7.t10.t20))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t16.t7.t10.t18 t2.t95.t16.t7.t10.t21))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t7.t10.t22 t2.t95.t16.t7.t10.t23))
% 0.85/1.08 (step t2.t95.t16.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t16.t7.t10.t24 t2.t95.t16.t7.t10.t25))
% 0.85/1.08 (step t2.t95.t16.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t16.t7.t9 t2.t95.t16.t7.t10))
% 0.85/1.08 (step t2.t95.t16.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t16.t7.t8 t2.t95.t16.t7.t11))
% 0.85/1.08 (step t2.t95.t16.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t16.t7.t5 t2.t95.t16.t7.t12 a4))
% 0.85/1.08 (step t2.t95.t16.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t16.t7.t4 t2.t95.t16.t7.t13 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t16.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t16.t7.t14))
% 0.85/1.08 (step t2.t95.t16.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t16.t7.t14))
% 0.85/1.08 (step t2.t95.t16.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t16.t7.t16 t2.t95.t16.t7.t17))
% 0.85/1.08 (step t2.t95.t16.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t16.t7.t15 t2.t95.t16.t7.t18))
% 0.85/1.08 (step t2.t95.t16.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t95.t16.t7.t19 t2.t95.t16.t7.t20))
% 0.85/1.08 (step t2.t95.t16.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t7.t21 t2.t95.t16.t7.t22))
% 0.85/1.08 (step t2.t95.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t95.t16.t6 t2.t95.t16.t7))
% 0.85/1.08 (step t2.t95.t16.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t16.t10.t4 t2.t95.t16.t10.t5))
% 0.85/1.08 (step t2.t95.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t16.t10.t8.t3 t2.t95.t16.t10.t8.t4))
% 0.85/1.08 (step t2.t95.t16.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t10.t7 t2.t95.t16.t10.t8))
% 0.85/1.08 (step t2.t95.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t10.t6 t2.t95.t16.t10.t9))
% 0.85/1.08 (step t2.t95.t16.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t95.t16.t10.t10 t2.t95.t16.t10.t11))
% 0.85/1.08 (step t2.t95.t16.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t10.t12 t2.t95.t16.t10.t13))
% 0.85/1.08 (step t2.t95.t16.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t10.t14 t2.t95.t16.t10.t15))
% 0.85/1.08 (step t2.t95.t16.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t95.t16.t10.t16 t2.t95.t16.t10.t17))
% 0.85/1.08 (step t2.t95.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t16.t9 t2.t95.t16.t10))
% 0.85/1.08 (step t2.t95.t16.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t16.t8 t2.t95.t16.t11))
% 0.85/1.08 (step t2.t95.t16.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t95.t16.t5 t2.t95.t16.t12 a5))
% 0.85/1.08 (step t2.t95.t16.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t16.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t16.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t16.t16.t4 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t16.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t16.t16.t5))
% 0.85/1.08 (step t2.t95.t16.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t16.t16.t5))
% 0.85/1.08 (step t2.t95.t16.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t16.t16.t6 t2.t95.t16.t16.t8))
% 0.85/1.08 (step t2.t95.t16.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t16.t16.t7 t2.t95.t16.t16.t9))
% 0.85/1.08 (step t2.t95.t16.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t16.t16.t6 t2.t95.t16.t16.t11))
% 0.85/1.08 (step t2.t95.t16.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t16.t16.t10 t2.t95.t16.t16.t12))
% 0.85/1.08 (step t2.t95.t16.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t16.t16.t6 t2.t95.t16.t16.t13))
% 0.85/1.08 (step t2.t95.t16.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t16.t14 t2.t95.t16.t16.t15))
% 0.85/1.08 (step t2.t95.t16.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t16.t15 t2.t95.t16.t16))
% 0.85/1.08 (step t2.t95.t16.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t16.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t16.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t16.t19.t5 t2.t95.t16.t19.t6))
% 0.85/1.08 (step t2.t95.t16.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t16.t19.t9.t3 t2.t95.t16.t19.t9.t4))
% 0.85/1.08 (step t2.t95.t16.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t19.t8 t2.t95.t16.t19.t9))
% 0.85/1.08 (step t2.t95.t16.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t16.t19.t7 t2.t95.t16.t19.t10))
% 0.85/1.08 (step t2.t95.t16.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t16.t19.t11 t2.t95.t16.t19.t12))
% 0.85/1.08 (step t2.t95.t16.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t16.t19.t15.t2 t2.t95.t16.t19.t15.t3))
% 0.85/1.08 (step t2.t95.t16.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t16.t19.t14 t2.t95.t16.t19.t15))
% 0.85/1.08 (step t2.t95.t16.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t16.t19.t13 t2.t95.t16.t19.t16))
% 0.85/1.08 (step t2.t95.t16.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t16.t19.t4 t2.t95.t16.t19.t17))
% 0.85/1.08 (step t2.t95.t16.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t16.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t16.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t16.t19.t20.t2))
% 0.85/1.08 (step t2.t95.t16.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t16.t19.t19 t2.t95.t16.t19.t20))
% 0.85/1.08 (step t2.t95.t16.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t16.t19.t18 t2.t95.t16.t19.t21))
% 0.85/1.08 (step t2.t95.t16.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t19.t22 t2.t95.t16.t19.t23))
% 0.85/1.08 (step t2.t95.t16.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t16.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t16.t19.t24 t2.t95.t16.t19.t25))
% 0.85/1.08 (step t2.t95.t16.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t16.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t16.t18 t2.t95.t16.t19))
% 0.85/1.08 (step t2.t95.t16.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t16.t17 t2.t95.t16.t20))
% 0.85/1.08 (step t2.t95.t16.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t16.t14 t2.t95.t16.t21 a4))
% 0.85/1.08 (step t2.t95.t16.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t16.t4 t2.t95.t16.t13 t2.t95.t16.t22 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t16.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t16.t23))
% 0.85/1.08 (step t2.t95.t16.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t16.t23))
% 0.85/1.08 (step t2.t95.t16.t26 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t16.t25 t2.t95.t16.t26))
% 0.85/1.08 (step t2.t95.t16.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t16.t24 t2.t95.t16.t27))
% 0.85/1.08 (step t2.t95.t16.t29 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t95.t16.t28 t2.t95.t16.t29))
% 0.85/1.08 (step t2.t95.t16.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t16.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t95.t16.t30 t2.t95.t16.t31))
% 0.85/1.08 (step t2.t95.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t17 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t95.t15 t2.t95.t16))
% 0.85/1.08 (step t2.t95.t18 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t19.t4 t2.t95.t19.t5))
% 0.85/1.08 (step t2.t95.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t19.t8.t3 t2.t95.t19.t8.t4))
% 0.85/1.08 (step t2.t95.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t19.t7 t2.t95.t19.t8))
% 0.85/1.08 (step t2.t95.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t19.t6 t2.t95.t19.t9))
% 0.85/1.08 (step t2.t95.t19.t11 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t95.t19.t10 t2.t95.t19.t11))
% 0.85/1.08 (step t2.t95.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t95.t19.t12 t2.t95.t19.t13))
% 0.85/1.08 (step t2.t95.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t19.t14 t2.t95.t19.t15))
% 0.85/1.08 (step t2.t95.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t95.t19.t16 t2.t95.t19.t17))
% 0.85/1.08 (step t2.t95.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.85/1.08 (step t2.t95.t20 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t95.t18 t2.t95.t19))
% 0.85/1.08 (step t2.t95.t21 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t95.t17 t2.t95.t20))
% 0.85/1.08 (step t2.t95.t22 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t95.t14 t2.t95.t21 a6))
% 0.85/1.08 (step t2.t95.t23 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t24 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t25.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t25.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t25.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t25.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t25.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t25.t7.t4 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t25.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t25.t7.t5))
% 0.85/1.08 (step t2.t95.t25.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t25.t7.t5))
% 0.85/1.08 (step t2.t95.t25.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t25.t7.t6 t2.t95.t25.t7.t8))
% 0.85/1.08 (step t2.t95.t25.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t25.t7.t7 t2.t95.t25.t7.t9))
% 0.85/1.08 (step t2.t95.t25.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t25.t7.t6 t2.t95.t25.t7.t11))
% 0.85/1.08 (step t2.t95.t25.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t25.t7.t10 t2.t95.t25.t7.t12))
% 0.85/1.08 (step t2.t95.t25.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t25.t7.t6 t2.t95.t25.t7.t13))
% 0.85/1.08 (step t2.t95.t25.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t25.t7.t14 t2.t95.t25.t7.t15))
% 0.85/1.08 (step t2.t95.t25.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t25.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t25.t6 t2.t95.t25.t7))
% 0.85/1.08 (step t2.t95.t25.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t25.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t25.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t25.t10.t5 t2.t95.t25.t10.t6))
% 0.85/1.08 (step t2.t95.t25.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t25.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t25.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t25.t10.t9.t3 t2.t95.t25.t10.t9.t4))
% 0.85/1.08 (step t2.t95.t25.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t25.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t25.t10.t8 t2.t95.t25.t10.t9))
% 0.85/1.08 (step t2.t95.t25.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t25.t10.t7 t2.t95.t25.t10.t10))
% 0.85/1.08 (step t2.t95.t25.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t25.t10.t11 t2.t95.t25.t10.t12))
% 0.85/1.08 (step t2.t95.t25.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t25.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t25.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t25.t10.t15.t2 t2.t95.t25.t10.t15.t3))
% 0.85/1.08 (step t2.t95.t25.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.08 (step t2.t95.t25.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t25.t10.t14 t2.t95.t25.t10.t15))
% 0.85/1.08 (step t2.t95.t25.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t25.t10.t13 t2.t95.t25.t10.t16))
% 0.85/1.08 (step t2.t95.t25.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t25.t10.t4 t2.t95.t25.t10.t17))
% 0.85/1.08 (step t2.t95.t25.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t25.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t25.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t25.t10.t20.t2))
% 0.85/1.08 (step t2.t95.t25.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t25.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t25.t10.t19 t2.t95.t25.t10.t20))
% 0.85/1.08 (step t2.t95.t25.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t25.t10.t18 t2.t95.t25.t10.t21))
% 0.85/1.08 (step t2.t95.t25.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t25.t10.t22 t2.t95.t25.t10.t23))
% 0.85/1.08 (step t2.t95.t25.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t25.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t25.t10.t24 t2.t95.t25.t10.t25))
% 0.85/1.08 (step t2.t95.t25.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.85/1.08 (step t2.t95.t25.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t25.t9 t2.t95.t25.t10))
% 0.85/1.08 (step t2.t95.t25.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t25.t8 t2.t95.t25.t11))
% 0.85/1.08 (step t2.t95.t25.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t25.t5 t2.t95.t25.t12 a4))
% 0.85/1.08 (step t2.t95.t25.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t25.t4 t2.t95.t25.t13 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t25.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t25.t14))
% 0.85/1.08 (step t2.t95.t25.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t25.t14))
% 0.85/1.08 (step t2.t95.t25.t17 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t25.t16 t2.t95.t25.t17))
% 0.85/1.08 (step t2.t95.t25.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t25.t15 t2.t95.t25.t18))
% 0.85/1.08 (step t2.t95.t25.t20 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t95.t25.t19 t2.t95.t25.t20))
% 0.85/1.08 (step t2.t95.t25.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t25.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t95.t25.t21 t2.t95.t25.t22))
% 0.85/1.08 (step t2.t95.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t26 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t95.t24 t2.t95.t25))
% 0.85/1.08 (step t2.t95.t27 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t28.t4 t2.t95.t28.t5))
% 0.85/1.08 (step t2.t95.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t28.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t28.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t8.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t28.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t28.t8.t3 t2.t95.t28.t8.t4))
% 0.85/1.08 (step t2.t95.t28.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t28.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t28.t7 t2.t95.t28.t8))
% 0.85/1.08 (step t2.t95.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t28.t6 t2.t95.t28.t9))
% 0.85/1.08 (step t2.t95.t28.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t95.t28.t10 t2.t95.t28.t11))
% 0.85/1.08 (step t2.t95.t28.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t28.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t28.t12 t2.t95.t28.t13))
% 0.85/1.08 (step t2.t95.t28.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t28.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t95.t28.t14 t2.t95.t28.t15))
% 0.85/1.08 (step t2.t95.t28.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t28.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t95.t28.t16 t2.t95.t28.t17))
% 0.85/1.08 (step t2.t95.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.85/1.08 (step t2.t95.t29 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t95.t27 t2.t95.t28))
% 0.85/1.08 (step t2.t95.t30 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t26 t2.t95.t29))
% 0.85/1.08 (step t2.t95.t31 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t95.t23 t2.t95.t30 a5))
% 0.85/1.08 (step t2.t95.t32 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.85/1.08 (step t2.t95.t33 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t34 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t34.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.85/1.08 (step t2.t95.t34.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t34.t4 a3 a2 a1 a0))
% 0.85/1.08 (step t2.t95.t34.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t34.t5))
% 0.85/1.08 (step t2.t95.t34.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t95.t34.t5))
% 0.85/1.08 (step t2.t95.t34.t8 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t95.t34.t6 t2.t95.t34.t8))
% 0.85/1.08 (step t2.t95.t34.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t95.t34.t7 t2.t95.t34.t9))
% 0.85/1.08 (step t2.t95.t34.t11 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t95.t34.t6 t2.t95.t34.t11))
% 0.85/1.08 (step t2.t95.t34.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t95.t34.t10 t2.t95.t34.t12))
% 0.85/1.08 (step t2.t95.t34.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t95.t34.t6 t2.t95.t34.t13))
% 0.85/1.08 (step t2.t95.t34.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t34.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t95.t34.t14 t2.t95.t34.t15))
% 0.85/1.08 (step t2.t95.t34 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.85/1.08 (step t2.t95.t35 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t95.t33 t2.t95.t34))
% 0.85/1.08 (step t2.t95.t36 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.85/1.08 (anchor :step t2.t95.t37 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.85/1.08 (step t2.t95.t37.t1 (cl (= Phi Phi)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t2 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t37.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t95.t37.t5 t2.t95.t37.t6))
% 0.85/1.08 (step t2.t95.t37.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t37.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t37.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t9.t2 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t37.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t95.t37.t9.t3 t2.t95.t37.t9.t4))
% 0.85/1.08 (step t2.t95.t37.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.85/1.08 (step t2.t95.t37.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t37.t8 t2.t95.t37.t9))
% 0.85/1.08 (step t2.t95.t37.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t95.t37.t7 t2.t95.t37.t10))
% 0.85/1.08 (step t2.t95.t37.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t37.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t37.t11 t2.t95.t37.t12))
% 0.85/1.08 (step t2.t95.t37.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t37.t15 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t37.t15.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t37.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t95.t37.t15.t2 t2.t95.t37.t15.t3))
% 0.85/1.08 (step t2.t95.t37.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.85/1.08 (step t2.t95.t37.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t37.t14 t2.t95.t37.t15))
% 0.85/1.08 (step t2.t95.t37.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t95.t37.t13 t2.t95.t37.t16))
% 0.85/1.08 (step t2.t95.t37.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t95.t37.t4 t2.t95.t37.t17))
% 0.85/1.08 (step t2.t95.t37.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.85/1.08 (anchor :step t2.t95.t37.t20 :args ((W $$unsorted) (:= W W)))
% 0.85/1.08 (step t2.t95.t37.t20.t1 (cl (= W W)) :rule refl)
% 0.85/1.08 (step t2.t95.t37.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.85/1.08 (step t2.t95.t37.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t95.t37.t20.t2))
% 0.90/1.08 (step t2.t95.t37.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t95.t37.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t37.t19 t2.t95.t37.t20))
% 0.90/1.08 (step t2.t95.t37.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t95.t37.t18 t2.t95.t37.t21))
% 0.90/1.08 (step t2.t95.t37.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t95.t37.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t95.t37.t22 t2.t95.t37.t23))
% 0.90/1.08 (step t2.t95.t37.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t95.t37.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t95.t37.t24 t2.t95.t37.t25))
% 0.90/1.08 (step t2.t95.t37 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t95.t38 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t95.t36 t2.t95.t37))
% 0.90/1.08 (step t2.t95.t39 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t95.t35 t2.t95.t38))
% 0.90/1.08 (step t2.t95.t40 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t95.t32 t2.t95.t39 a4))
% 0.90/1.08 (step t2.t95.t41 (cl (and (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t95.t4 t2.t95.t13 t2.t95.t22 t2.t95.t31 t2.t95.t40 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t95.t42 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t95.t41))
% 0.90/1.08 (step t2.t95.t43 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule and :premises (t2.t95.t41))
% 0.90/1.08 (step t2.t95.t44 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t95.t45 (cl (= (@ tptp.mequiv Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi))) :rule cong :premises (t2.t95.t43 t2.t95.t44))
% 0.90/1.08 (step t2.t95.t46 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t95.t47 (cl (= (@ (@ tptp.mequiv Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi))) :rule cong :premises (t2.t95.t45 t2.t95.t46))
% 0.90/1.08 (step t2.t95.t48 (cl (= (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)))) :rule cong :premises (t2.t95.t42 t2.t95.t47))
% 0.90/1.08 (step t2.t95.t49 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t95.t50 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) :rule cong :premises (t2.t95.t48 t2.t95.t49))
% 0.90/1.08 (step t2.t95 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t96 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))))) :rule cong :premises (t2.t94 t2.t95))
% 0.90/1.08 (step t2.t97 (cl (= tptp.mxor tptp.mxor)) :rule refl)
% 0.90/1.08 (anchor :step t2.t98 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t98.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t98.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t98.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t98.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t98.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.90/1.08 (step t2.t98.t6 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t98.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi))) :rule cong :premises (t2.t98.t5 t2.t98.t6))
% 0.90/1.08 (step t2.t98.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule all_simplify)
% 0.90/1.08 (step t2.t98.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t98.t7 t2.t98.t8))
% 0.90/1.08 (step t2.t98.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t98.t4 t2.t98.t9))
% 0.90/1.08 (step t2.t98.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t98.t12 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t98.t12.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t98.t12.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W) (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule all_simplify)
% 0.90/1.08 (step t2.t98.t12.t3 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))))) :rule cong :premises (t2.t98.t12.t2))
% 0.90/1.08 (step t2.t98.t12.t4 (cl (= (not (not (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t98.t12.t5 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W)))))) :rule trans :premises (t2.t98.t12.t3 t2.t98.t12.t4))
% 0.90/1.08 (step t2.t98.t12 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) W))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule bind)
% 0.90/1.08 (step t2.t98.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t98.t11 t2.t98.t12))
% 0.90/1.08 (step t2.t98.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))))) :rule trans :premises (t2.t98.t10 t2.t98.t13))
% 0.90/1.08 (step t2.t98.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t98.t16 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0))) :rule cong :premises (t2.t98.t14 t2.t98.t15))
% 0.90/1.08 (step t2.t98.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (or (not (@ Phi W)) (@ Psi W))) (not (or (not (@ Psi W)) (@ Phi W))))) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t98.t18 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t98.t16 t2.t98.t17))
% 0.90/1.08 (step t2.t98 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t99 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule cong :premises (t2.t97 t2.t98))
% 0.90/1.08 (step t2.t100 (cl (= (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t96 t2.t99))
% 0.90/1.08 (step t2.t101 (cl (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule resolution :premises (t2.t93 t2.t100 a8))
% 0.90/1.08 (step t2.t102 (cl (not (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) (not (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t103 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t4 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t5 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t6 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t7.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t7.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t7.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t7.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t7.t7.t7.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t7.t7.t7.t5))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t7.t7.t7.t5))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t7.t7.t7.t6 t2.t104.t7.t7.t7.t8))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t7.t7.t7.t7 t2.t104.t7.t7.t7.t9))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t104.t7.t7.t7.t6 t2.t104.t7.t7.t7.t11))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t104.t7.t7.t7.t10 t2.t104.t7.t7.t7.t12))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t104.t7.t7.t7.t6 t2.t104.t7.t7.t7.t13))
% 0.90/1.08 (step t2.t104.t7.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t7.t7.t14 t2.t104.t7.t7.t7.t15))
% 0.90/1.08 (step t2.t104.t7.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t104.t7.t7.t6 t2.t104.t7.t7.t7))
% 0.90/1.08 (step t2.t104.t7.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t7.t7.t10.t5 t2.t104.t7.t7.t10.t6))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t7.t7.t10.t9.t3 t2.t104.t7.t7.t10.t9.t4))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t7.t10.t8 t2.t104.t7.t7.t10.t9))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t7.t10.t7 t2.t104.t7.t7.t10.t10))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t7.t7.t10.t11 t2.t104.t7.t7.t10.t12))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t104.t7.t7.t10.t15.t2 t2.t104.t7.t7.t10.t15.t3))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t7.t7.t10.t14 t2.t104.t7.t7.t10.t15))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t7.t7.t10.t13 t2.t104.t7.t7.t10.t16))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t104.t7.t7.t10.t4 t2.t104.t7.t7.t10.t17))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t7.t7.t10.t20.t2))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t7.t7.t10.t19 t2.t104.t7.t7.t10.t20))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t7.t7.t10.t18 t2.t104.t7.t7.t10.t21))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t7.t10.t22 t2.t104.t7.t7.t10.t23))
% 0.90/1.08 (step t2.t104.t7.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t7.t7.t10.t24 t2.t104.t7.t7.t10.t25))
% 0.90/1.08 (step t2.t104.t7.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t104.t7.t7.t9 t2.t104.t7.t7.t10))
% 0.90/1.08 (step t2.t104.t7.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t104.t7.t7.t8 t2.t104.t7.t7.t11))
% 0.90/1.08 (step t2.t104.t7.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t104.t7.t7.t5 t2.t104.t7.t7.t12 a4))
% 0.90/1.08 (step t2.t104.t7.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t7.t7.t4 t2.t104.t7.t7.t13 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t7.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t7.t7.t14))
% 0.90/1.08 (step t2.t104.t7.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t7.t7.t14))
% 0.90/1.08 (step t2.t104.t7.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t7.t7.t16 t2.t104.t7.t7.t17))
% 0.90/1.08 (step t2.t104.t7.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t7.t7.t15 t2.t104.t7.t7.t18))
% 0.90/1.08 (step t2.t104.t7.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t104.t7.t7.t19 t2.t104.t7.t7.t20))
% 0.90/1.08 (step t2.t104.t7.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t7.t21 t2.t104.t7.t7.t22))
% 0.90/1.08 (step t2.t104.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t104.t7.t6 t2.t104.t7.t7))
% 0.90/1.08 (step t2.t104.t7.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t7.t10.t4 t2.t104.t7.t10.t5))
% 0.90/1.08 (step t2.t104.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t7.t10.t8.t3 t2.t104.t7.t10.t8.t4))
% 0.90/1.08 (step t2.t104.t7.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t10.t7 t2.t104.t7.t10.t8))
% 0.90/1.08 (step t2.t104.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t10.t6 t2.t104.t7.t10.t9))
% 0.90/1.08 (step t2.t104.t7.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t104.t7.t10.t10 t2.t104.t7.t10.t11))
% 0.90/1.08 (step t2.t104.t7.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t10.t12 t2.t104.t7.t10.t13))
% 0.90/1.08 (step t2.t104.t7.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t10.t14 t2.t104.t7.t10.t15))
% 0.90/1.08 (step t2.t104.t7.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t104.t7.t10.t16 t2.t104.t7.t10.t17))
% 0.90/1.08 (step t2.t104.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t104.t7.t9 t2.t104.t7.t10))
% 0.90/1.08 (step t2.t104.t7.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t7.t8 t2.t104.t7.t11))
% 0.90/1.08 (step t2.t104.t7.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t104.t7.t5 t2.t104.t7.t12 a5))
% 0.90/1.08 (step t2.t104.t7.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t7.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t7.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t7.t16.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t7.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t7.t16.t5))
% 0.90/1.08 (step t2.t104.t7.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t7.t16.t5))
% 0.90/1.08 (step t2.t104.t7.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t7.t16.t6 t2.t104.t7.t16.t8))
% 0.90/1.08 (step t2.t104.t7.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t7.t16.t7 t2.t104.t7.t16.t9))
% 0.90/1.08 (step t2.t104.t7.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t104.t7.t16.t6 t2.t104.t7.t16.t11))
% 0.90/1.08 (step t2.t104.t7.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t104.t7.t16.t10 t2.t104.t7.t16.t12))
% 0.90/1.08 (step t2.t104.t7.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t104.t7.t16.t6 t2.t104.t7.t16.t13))
% 0.90/1.08 (step t2.t104.t7.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t16.t14 t2.t104.t7.t16.t15))
% 0.90/1.08 (step t2.t104.t7.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t104.t7.t15 t2.t104.t7.t16))
% 0.90/1.08 (step t2.t104.t7.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t7.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t7.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t7.t19.t5 t2.t104.t7.t19.t6))
% 0.90/1.08 (step t2.t104.t7.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t7.t19.t9.t3 t2.t104.t7.t19.t9.t4))
% 0.90/1.08 (step t2.t104.t7.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t19.t8 t2.t104.t7.t19.t9))
% 0.90/1.08 (step t2.t104.t7.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t7.t19.t7 t2.t104.t7.t19.t10))
% 0.90/1.08 (step t2.t104.t7.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t7.t19.t11 t2.t104.t7.t19.t12))
% 0.90/1.08 (step t2.t104.t7.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t104.t7.t19.t15.t2 t2.t104.t7.t19.t15.t3))
% 0.90/1.08 (step t2.t104.t7.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t7.t19.t14 t2.t104.t7.t19.t15))
% 0.90/1.08 (step t2.t104.t7.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t7.t19.t13 t2.t104.t7.t19.t16))
% 0.90/1.08 (step t2.t104.t7.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t104.t7.t19.t4 t2.t104.t7.t19.t17))
% 0.90/1.08 (step t2.t104.t7.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t7.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t7.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t7.t19.t20.t2))
% 0.90/1.08 (step t2.t104.t7.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t7.t19.t19 t2.t104.t7.t19.t20))
% 0.90/1.08 (step t2.t104.t7.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t7.t19.t18 t2.t104.t7.t19.t21))
% 0.90/1.08 (step t2.t104.t7.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t19.t22 t2.t104.t7.t19.t23))
% 0.90/1.08 (step t2.t104.t7.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t7.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t7.t19.t24 t2.t104.t7.t19.t25))
% 0.90/1.08 (step t2.t104.t7.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t7.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t104.t7.t18 t2.t104.t7.t19))
% 0.90/1.08 (step t2.t104.t7.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t104.t7.t17 t2.t104.t7.t20))
% 0.90/1.08 (step t2.t104.t7.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t104.t7.t14 t2.t104.t7.t21 a4))
% 0.90/1.08 (step t2.t104.t7.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t7.t4 t2.t104.t7.t13 t2.t104.t7.t22 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t7.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t7.t23))
% 0.90/1.08 (step t2.t104.t7.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t7.t23))
% 0.90/1.08 (step t2.t104.t7.t26 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t104.t7.t25 t2.t104.t7.t26))
% 0.90/1.08 (step t2.t104.t7.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t104.t7.t24 t2.t104.t7.t27))
% 0.90/1.08 (step t2.t104.t7.t29 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t104.t7.t28 t2.t104.t7.t29))
% 0.90/1.08 (step t2.t104.t7.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t7.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t104.t7.t30 t2.t104.t7.t31))
% 0.90/1.08 (step t2.t104.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t8 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t104.t6 t2.t104.t7))
% 0.90/1.08 (step t2.t104.t9 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t10.t4 t2.t104.t10.t5))
% 0.90/1.08 (step t2.t104.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t10.t8.t3 t2.t104.t10.t8.t4))
% 0.90/1.08 (step t2.t104.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t10.t7 t2.t104.t10.t8))
% 0.90/1.08 (step t2.t104.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t10.t6 t2.t104.t10.t9))
% 0.90/1.08 (step t2.t104.t10.t11 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t104.t10.t10 t2.t104.t10.t11))
% 0.90/1.08 (step t2.t104.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t104.t10.t12 t2.t104.t10.t13))
% 0.90/1.08 (step t2.t104.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t104.t10.t14 t2.t104.t10.t15))
% 0.90/1.08 (step t2.t104.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t104.t10.t16 t2.t104.t10.t17))
% 0.90/1.08 (step t2.t104.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t104.t11 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t104.t9 t2.t104.t10))
% 0.90/1.08 (step t2.t104.t12 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t104.t8 t2.t104.t11))
% 0.90/1.08 (step t2.t104.t13 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t104.t5 t2.t104.t12 a6))
% 0.90/1.08 (step t2.t104.t14 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t15 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t16.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t16.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t16.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t16.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t16.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t16.t7.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t16.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t16.t7.t5))
% 0.90/1.08 (step t2.t104.t16.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t16.t7.t5))
% 0.90/1.08 (step t2.t104.t16.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t16.t7.t6 t2.t104.t16.t7.t8))
% 0.90/1.08 (step t2.t104.t16.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t16.t7.t7 t2.t104.t16.t7.t9))
% 0.90/1.08 (step t2.t104.t16.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t104.t16.t7.t6 t2.t104.t16.t7.t11))
% 0.90/1.08 (step t2.t104.t16.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t104.t16.t7.t10 t2.t104.t16.t7.t12))
% 0.90/1.08 (step t2.t104.t16.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t104.t16.t7.t6 t2.t104.t16.t7.t13))
% 0.90/1.08 (step t2.t104.t16.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t104.t16.t7.t14 t2.t104.t16.t7.t15))
% 0.90/1.08 (step t2.t104.t16.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t16.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t104.t16.t6 t2.t104.t16.t7))
% 0.90/1.08 (step t2.t104.t16.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t16.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t16.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t16.t10.t5 t2.t104.t16.t10.t6))
% 0.90/1.08 (step t2.t104.t16.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t16.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t16.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t16.t10.t9.t3 t2.t104.t16.t10.t9.t4))
% 0.90/1.08 (step t2.t104.t16.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t16.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t16.t10.t8 t2.t104.t16.t10.t9))
% 0.90/1.08 (step t2.t104.t16.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t16.t10.t7 t2.t104.t16.t10.t10))
% 0.90/1.08 (step t2.t104.t16.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t16.t10.t11 t2.t104.t16.t10.t12))
% 0.90/1.08 (step t2.t104.t16.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t16.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t16.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t104.t16.t10.t15.t2 t2.t104.t16.t10.t15.t3))
% 0.90/1.08 (step t2.t104.t16.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t104.t16.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t16.t10.t14 t2.t104.t16.t10.t15))
% 0.90/1.08 (step t2.t104.t16.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t16.t10.t13 t2.t104.t16.t10.t16))
% 0.90/1.08 (step t2.t104.t16.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t104.t16.t10.t4 t2.t104.t16.t10.t17))
% 0.90/1.08 (step t2.t104.t16.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t16.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t16.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t16.t10.t20.t2))
% 0.90/1.08 (step t2.t104.t16.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t16.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t16.t10.t19 t2.t104.t16.t10.t20))
% 0.90/1.08 (step t2.t104.t16.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t16.t10.t18 t2.t104.t16.t10.t21))
% 0.90/1.08 (step t2.t104.t16.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t104.t16.t10.t22 t2.t104.t16.t10.t23))
% 0.90/1.08 (step t2.t104.t16.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t16.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t16.t10.t24 t2.t104.t16.t10.t25))
% 0.90/1.08 (step t2.t104.t16.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t16.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t104.t16.t9 t2.t104.t16.t10))
% 0.90/1.08 (step t2.t104.t16.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t104.t16.t8 t2.t104.t16.t11))
% 0.90/1.08 (step t2.t104.t16.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t104.t16.t5 t2.t104.t16.t12 a4))
% 0.90/1.08 (step t2.t104.t16.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t16.t4 t2.t104.t16.t13 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t16.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t16.t14))
% 0.90/1.08 (step t2.t104.t16.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t16.t14))
% 0.90/1.08 (step t2.t104.t16.t17 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t16.t16 t2.t104.t16.t17))
% 0.90/1.08 (step t2.t104.t16.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t16.t15 t2.t104.t16.t18))
% 0.90/1.08 (step t2.t104.t16.t20 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t104.t16.t19 t2.t104.t16.t20))
% 0.90/1.08 (step t2.t104.t16.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t16.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t104.t16.t21 t2.t104.t16.t22))
% 0.90/1.08 (step t2.t104.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t17 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t104.t15 t2.t104.t16))
% 0.90/1.08 (step t2.t104.t18 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t19.t4 t2.t104.t19.t5))
% 0.90/1.08 (step t2.t104.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t19.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t19.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t19.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t19.t8.t3 t2.t104.t19.t8.t4))
% 0.90/1.08 (step t2.t104.t19.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t19.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t19.t7 t2.t104.t19.t8))
% 0.90/1.08 (step t2.t104.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t19.t6 t2.t104.t19.t9))
% 0.90/1.08 (step t2.t104.t19.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t104.t19.t10 t2.t104.t19.t11))
% 0.90/1.08 (step t2.t104.t19.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t19.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t19.t12 t2.t104.t19.t13))
% 0.90/1.08 (step t2.t104.t19.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t19.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t104.t19.t14 t2.t104.t19.t15))
% 0.90/1.08 (step t2.t104.t19.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t19.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t104.t19.t16 t2.t104.t19.t17))
% 0.90/1.08 (step t2.t104.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t104.t20 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t104.t18 t2.t104.t19))
% 0.90/1.08 (step t2.t104.t21 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t17 t2.t104.t20))
% 0.90/1.08 (step t2.t104.t22 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t104.t14 t2.t104.t21 a5))
% 0.90/1.08 (step t2.t104.t23 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t104.t24 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t25 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t25.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t104.t25.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t25.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t25.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t104.t25.t5))
% 0.90/1.08 (step t2.t104.t25.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t104.t25.t5))
% 0.90/1.08 (step t2.t104.t25.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t104.t25.t6 t2.t104.t25.t8))
% 0.90/1.08 (step t2.t104.t25.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t104.t25.t7 t2.t104.t25.t9))
% 0.90/1.08 (step t2.t104.t25.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t104.t25.t6 t2.t104.t25.t11))
% 0.90/1.08 (step t2.t104.t25.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t104.t25.t10 t2.t104.t25.t12))
% 0.90/1.08 (step t2.t104.t25.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t104.t25.t6 t2.t104.t25.t13))
% 0.90/1.08 (step t2.t104.t25.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t25.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t104.t25.t14 t2.t104.t25.t15))
% 0.90/1.08 (step t2.t104.t25 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t104.t26 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t104.t24 t2.t104.t25))
% 0.90/1.08 (step t2.t104.t27 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t104.t28 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t104.t28.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t104.t28.t5 t2.t104.t28.t6))
% 0.90/1.08 (step t2.t104.t28.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t28.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t28.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t104.t28.t9.t3 t2.t104.t28.t9.t4))
% 0.90/1.08 (step t2.t104.t28.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t104.t28.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t28.t8 t2.t104.t28.t9))
% 0.90/1.08 (step t2.t104.t28.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t104.t28.t7 t2.t104.t28.t10))
% 0.90/1.08 (step t2.t104.t28.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t28.t11 t2.t104.t28.t12))
% 0.90/1.08 (step t2.t104.t28.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t28.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t28.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t104.t28.t15.t2 t2.t104.t28.t15.t3))
% 0.90/1.08 (step t2.t104.t28.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t104.t28.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t28.t14 t2.t104.t28.t15))
% 0.90/1.08 (step t2.t104.t28.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t104.t28.t13 t2.t104.t28.t16))
% 0.90/1.08 (step t2.t104.t28.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t104.t28.t4 t2.t104.t28.t17))
% 0.90/1.08 (step t2.t104.t28.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t104.t28.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t104.t28.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t104.t28.t20.t2))
% 0.90/1.08 (step t2.t104.t28.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t28.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t28.t19 t2.t104.t28.t20))
% 0.90/1.08 (step t2.t104.t28.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t104.t28.t18 t2.t104.t28.t21))
% 0.90/1.08 (step t2.t104.t28.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t28.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t104.t28.t22 t2.t104.t28.t23))
% 0.90/1.08 (step t2.t104.t28.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t104.t28.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t104.t28.t24 t2.t104.t28.t25))
% 0.90/1.08 (step t2.t104.t28 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t104.t29 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t104.t27 t2.t104.t28))
% 0.90/1.08 (step t2.t104.t30 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t104.t26 t2.t104.t29))
% 0.90/1.08 (step t2.t104.t31 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t104.t23 t2.t104.t30 a4))
% 0.90/1.08 (step t2.t104.t32 (cl (and (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t104.t4 t2.t104.t13 t2.t104.t22 t2.t104.t31 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t104.t33 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t104.t32))
% 0.90/1.08 (step t2.t104.t34 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t104.t32))
% 0.90/1.08 (step t2.t104.t35 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t104.t36 (cl (= (@ tptp.mimplies Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t104.t34 t2.t104.t35))
% 0.90/1.08 (step t2.t104.t37 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t104.t38 (cl (= (@ (@ tptp.mimplies Phi) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi))) :rule cong :premises (t2.t104.t36 t2.t104.t37))
% 0.90/1.08 (step t2.t104.t39 (cl (= (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)))) :rule cong :premises (t2.t104.t33 t2.t104.t38))
% 0.90/1.08 (step t2.t104.t40 (cl (= (@ tptp.mimplies Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t104.t34 t2.t104.t37))
% 0.90/1.08 (step t2.t104.t41 (cl (= (@ (@ tptp.mimplies Psi) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi))) :rule cong :premises (t2.t104.t40 t2.t104.t35))
% 0.90/1.08 (step t2.t104.t42 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)))) :rule cong :premises (t2.t104.t39 t2.t104.t41))
% 0.90/1.08 (step t2.t104.t43 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t104.t44 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) :rule cong :premises (t2.t104.t42 t2.t104.t43))
% 0.90/1.08 (step t2.t104 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t105 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))))) :rule cong :premises (t2.t103 t2.t104))
% 0.90/1.08 (step t2.t106 (cl (= tptp.mequiv tptp.mequiv)) :rule refl)
% 0.90/1.08 (anchor :step t2.t107 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t107.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t107.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t107.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t107.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule refl)
% 0.90/1.08 (step t2.t107.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t6 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t107.t7 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi))) :rule cong :premises (t2.t107.t5 t2.t107.t6))
% 0.90/1.08 (step t2.t107.t8 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t9 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule trans :premises (t2.t107.t7 t2.t107.t8))
% 0.90/1.08 (step t2.t107.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t107.t4 t2.t107.t9))
% 0.90/1.08 (step t2.t107.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t107.t12 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t107.t12.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t107.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t107.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t12.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t107.t12.t3))
% 0.90/1.08 (step t2.t107.t12.t5 (cl (= (not (@ Psi __flatten_var_0)) (not (@ Psi __flatten_var_0)))) :rule refl)
% 0.90/1.08 (step t2.t107.t12.t6 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) :rule cong :premises (t2.t107.t12.t4 t2.t107.t12.t5))
% 0.90/1.08 (step t2.t107.t12.t7 (cl (= (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t107.t12.t6))
% 0.90/1.08 (step t2.t107.t12 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t107.t13 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t107.t11 t2.t107.t12))
% 0.90/1.08 (step t2.t107.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))))) :rule trans :premises (t2.t107.t10 t2.t107.t13))
% 0.90/1.08 (step t2.t107.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t16 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t107.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi))) :rule cong :premises (t2.t107.t15 t2.t107.t16))
% 0.90/1.08 (step t2.t107.t18 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t19 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule trans :premises (t2.t107.t17 t2.t107.t18))
% 0.90/1.08 (step t2.t107.t20 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t107.t14 t2.t107.t19))
% 0.90/1.08 (step t2.t107.t21 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t107.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t107.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t107.t22.t2 (cl (= (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.90/1.08 (step t2.t107.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t22.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule cong :premises (t2.t107.t22.t3))
% 0.90/1.08 (step t2.t107.t22.t5 (cl (= (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t107.t22.t2 t2.t107.t22.t4))
% 0.90/1.08 (step t2.t107.t22.t6 (cl (= (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0)))) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule cong :premises (t2.t107.t22.t5))
% 0.90/1.08 (step t2.t107.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.90/1.08 (step t2.t107.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (@ Psi __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t107.t21 t2.t107.t22))
% 0.90/1.08 (step t2.t107.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule trans :premises (t2.t107.t20 t2.t107.t23))
% 0.90/1.08 (step t2.t107.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t107.t26 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0))) :rule cong :premises (t2.t107.t24 t2.t107.t25))
% 0.90/1.08 (step t2.t107.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (step t2.t107.t28 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) :rule trans :premises (t2.t107.t26 t2.t107.t27))
% 0.90/1.08 (step t2.t107 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule bind)
% 0.90/1.08 (step t2.t108 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Phi) Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule cong :premises (t2.t106 t2.t107))
% 0.90/1.08 (step t2.t109 (cl (= (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))))) :rule trans :premises (t2.t105 t2.t108))
% 0.90/1.08 (step t2.t110 (cl (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))))) :rule resolution :premises (t2.t102 t2.t109 a7))
% 0.90/1.08 (step t2.t111 (cl (not (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (not (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t112 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t4 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t113.t5 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t113.t6 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t113.t7.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t113.t7.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t7.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t7.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t113.t7.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t113.t7.t7.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t113.t7.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t113.t7.t7.t5))
% 0.90/1.08 (step t2.t113.t7.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t113.t7.t7.t5))
% 0.90/1.08 (step t2.t113.t7.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t113.t7.t7.t6 t2.t113.t7.t7.t8))
% 0.90/1.08 (step t2.t113.t7.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t113.t7.t7.t7 t2.t113.t7.t7.t9))
% 0.90/1.08 (step t2.t113.t7.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t113.t7.t7.t6 t2.t113.t7.t7.t11))
% 0.90/1.08 (step t2.t113.t7.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t113.t7.t7.t10 t2.t113.t7.t7.t12))
% 0.90/1.08 (step t2.t113.t7.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t113.t7.t7.t6 t2.t113.t7.t7.t13))
% 0.90/1.08 (step t2.t113.t7.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t113.t7.t7.t14 t2.t113.t7.t7.t15))
% 0.90/1.08 (step t2.t113.t7.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t113.t7.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t113.t7.t6 t2.t113.t7.t7))
% 0.90/1.08 (step t2.t113.t7.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t7.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t7.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t113.t7.t10.t5 t2.t113.t7.t10.t6))
% 0.90/1.08 (step t2.t113.t7.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t7.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t7.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t113.t7.t10.t9.t3 t2.t113.t7.t10.t9.t4))
% 0.90/1.08 (step t2.t113.t7.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t113.t7.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t7.t10.t8 t2.t113.t7.t10.t9))
% 0.90/1.08 (step t2.t113.t7.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t7.t10.t7 t2.t113.t7.t10.t10))
% 0.90/1.08 (step t2.t113.t7.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t113.t7.t10.t11 t2.t113.t7.t10.t12))
% 0.90/1.08 (step t2.t113.t7.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t7.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t7.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t113.t7.t10.t15.t2 t2.t113.t7.t10.t15.t3))
% 0.90/1.08 (step t2.t113.t7.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t113.t7.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t113.t7.t10.t14 t2.t113.t7.t10.t15))
% 0.90/1.08 (step t2.t113.t7.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t113.t7.t10.t13 t2.t113.t7.t10.t16))
% 0.90/1.08 (step t2.t113.t7.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t113.t7.t10.t4 t2.t113.t7.t10.t17))
% 0.90/1.08 (step t2.t113.t7.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t7.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t7.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t113.t7.t10.t20.t2))
% 0.90/1.08 (step t2.t113.t7.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t113.t7.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t113.t7.t10.t19 t2.t113.t7.t10.t20))
% 0.90/1.08 (step t2.t113.t7.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t113.t7.t10.t18 t2.t113.t7.t10.t21))
% 0.90/1.08 (step t2.t113.t7.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t113.t7.t10.t22 t2.t113.t7.t10.t23))
% 0.90/1.08 (step t2.t113.t7.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t7.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t113.t7.t10.t24 t2.t113.t7.t10.t25))
% 0.90/1.08 (step t2.t113.t7.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t113.t7.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t113.t7.t9 t2.t113.t7.t10))
% 0.90/1.08 (step t2.t113.t7.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t113.t7.t8 t2.t113.t7.t11))
% 0.90/1.08 (step t2.t113.t7.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t113.t7.t5 t2.t113.t7.t12 a4))
% 0.90/1.08 (step t2.t113.t7.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t113.t7.t4 t2.t113.t7.t13 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t113.t7.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t113.t7.t14))
% 0.90/1.08 (step t2.t113.t7.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t113.t7.t14))
% 0.90/1.08 (step t2.t113.t7.t17 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t113.t7.t16 t2.t113.t7.t17))
% 0.90/1.08 (step t2.t113.t7.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t113.t7.t15 t2.t113.t7.t18))
% 0.90/1.08 (step t2.t113.t7.t20 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t113.t7.t19 t2.t113.t7.t20))
% 0.90/1.08 (step t2.t113.t7.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t7.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t113.t7.t21 t2.t113.t7.t22))
% 0.90/1.08 (step t2.t113.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t113.t8 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t113.t6 t2.t113.t7))
% 0.90/1.08 (step t2.t113.t9 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t113.t10.t4 t2.t113.t10.t5))
% 0.90/1.08 (step t2.t113.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t10.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t10.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t10.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t113.t10.t8.t3 t2.t113.t10.t8.t4))
% 0.90/1.08 (step t2.t113.t10.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t113.t10.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t10.t7 t2.t113.t10.t8))
% 0.90/1.08 (step t2.t113.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t10.t6 t2.t113.t10.t9))
% 0.90/1.08 (step t2.t113.t10.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t113.t10.t10 t2.t113.t10.t11))
% 0.90/1.08 (step t2.t113.t10.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t10.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t10.t12 t2.t113.t10.t13))
% 0.90/1.08 (step t2.t113.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t10.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t113.t10.t14 t2.t113.t10.t15))
% 0.90/1.08 (step t2.t113.t10.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t10.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t113.t10.t16 t2.t113.t10.t17))
% 0.90/1.08 (step t2.t113.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t113.t11 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t113.t9 t2.t113.t10))
% 0.90/1.08 (step t2.t113.t12 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t113.t8 t2.t113.t11))
% 0.90/1.08 (step t2.t113.t13 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t113.t5 t2.t113.t12 a5))
% 0.90/1.08 (step t2.t113.t14 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t113.t15 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t16 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t16.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t113.t16.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t113.t16.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t113.t16.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t113.t16.t5))
% 0.90/1.08 (step t2.t113.t16.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t113.t16.t5))
% 0.90/1.08 (step t2.t113.t16.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t113.t16.t6 t2.t113.t16.t8))
% 0.90/1.08 (step t2.t113.t16.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t113.t16.t7 t2.t113.t16.t9))
% 0.90/1.08 (step t2.t113.t16.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t113.t16.t6 t2.t113.t16.t11))
% 0.90/1.08 (step t2.t113.t16.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t113.t16.t10 t2.t113.t16.t12))
% 0.90/1.08 (step t2.t113.t16.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t113.t16.t6 t2.t113.t16.t13))
% 0.90/1.08 (step t2.t113.t16.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t16.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t113.t16.t14 t2.t113.t16.t15))
% 0.90/1.08 (step t2.t113.t16 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t113.t17 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t113.t15 t2.t113.t16))
% 0.90/1.08 (step t2.t113.t18 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t113.t19 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t113.t19.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t113.t19.t5 t2.t113.t19.t6))
% 0.90/1.08 (step t2.t113.t19.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t19.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t19.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t113.t19.t9.t3 t2.t113.t19.t9.t4))
% 0.90/1.08 (step t2.t113.t19.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t113.t19.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t19.t8 t2.t113.t19.t9))
% 0.90/1.08 (step t2.t113.t19.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t113.t19.t7 t2.t113.t19.t10))
% 0.90/1.08 (step t2.t113.t19.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t113.t19.t11 t2.t113.t19.t12))
% 0.90/1.08 (step t2.t113.t19.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t19.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t19.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t113.t19.t15.t2 t2.t113.t19.t15.t3))
% 0.90/1.08 (step t2.t113.t19.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t113.t19.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t113.t19.t14 t2.t113.t19.t15))
% 0.90/1.08 (step t2.t113.t19.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t113.t19.t13 t2.t113.t19.t16))
% 0.90/1.08 (step t2.t113.t19.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t113.t19.t4 t2.t113.t19.t17))
% 0.90/1.08 (step t2.t113.t19.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t113.t19.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t113.t19.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t113.t19.t20.t2))
% 0.90/1.08 (step t2.t113.t19.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t113.t19.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t113.t19.t19 t2.t113.t19.t20))
% 0.90/1.08 (step t2.t113.t19.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t113.t19.t18 t2.t113.t19.t21))
% 0.90/1.08 (step t2.t113.t19.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t19.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t113.t19.t22 t2.t113.t19.t23))
% 0.90/1.08 (step t2.t113.t19.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t113.t19.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t113.t19.t24 t2.t113.t19.t25))
% 0.90/1.08 (step t2.t113.t19 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t113.t20 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t113.t18 t2.t113.t19))
% 0.90/1.08 (step t2.t113.t21 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t113.t17 t2.t113.t20))
% 0.90/1.08 (step t2.t113.t22 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t113.t14 t2.t113.t21 a4))
% 0.90/1.08 (step t2.t113.t23 (cl (and (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t113.t4 t2.t113.t13 t2.t113.t22 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t113.t24 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t113.t23))
% 0.90/1.08 (step t2.t113.t25 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t113.t23))
% 0.90/1.08 (step t2.t113.t26 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t113.t27 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t113.t25 t2.t113.t26))
% 0.90/1.08 (step t2.t113.t28 (cl (= (@ tptp.mor (@ tptp.mnot Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t113.t24 t2.t113.t27))
% 0.90/1.08 (step t2.t113.t29 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t113.t30 (cl (= (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi))) :rule cong :premises (t2.t113.t28 t2.t113.t29))
% 0.90/1.08 (step t2.t113.t31 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t113.t32 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) :rule cong :premises (t2.t113.t30 t2.t113.t31))
% 0.90/1.08 (step t2.t113 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t114 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))))) :rule cong :premises (t2.t112 t2.t113))
% 0.90/1.08 (step t2.t115 (cl (= tptp.mimplied tptp.mimplied)) :rule refl)
% 0.90/1.08 (anchor :step t2.t116 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t116.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t116.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t116.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t116.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t116.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t116.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t116.t4 t2.t116.t5))
% 0.90/1.08 (step t2.t116.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t116.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t116.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t116.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t116.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t116.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t116.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W)) (or (not (@ Psi W)) (@ Psi W)))) :rule cong :premises (t2.t116.t8.t3 t2.t116.t8.t4))
% 0.90/1.08 (step t2.t116.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t116.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t116.t7 t2.t116.t8))
% 0.90/1.08 (step t2.t116.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))))) :rule trans :premises (t2.t116.t6 t2.t116.t9))
% 0.90/1.08 (step t2.t116.t11 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t116.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi))) :rule cong :premises (t2.t116.t10 t2.t116.t11))
% 0.90/1.08 (step t2.t116.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Psi W)) (@ Psi W))) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t116.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))))) :rule trans :premises (t2.t116.t12 t2.t116.t13))
% 0.90/1.08 (step t2.t116.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t116.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0))) :rule cong :premises (t2.t116.t14 t2.t116.t15))
% 0.90/1.08 (step t2.t116.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Psi W)) (@ Phi W))) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t116.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) :rule trans :premises (t2.t116.t16 t2.t116.t17))
% 0.90/1.08 (step t2.t116 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t117 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule cong :premises (t2.t115 t2.t116))
% 0.90/1.08 (step t2.t118 (cl (= (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) :rule trans :premises (t2.t114 t2.t117))
% 0.90/1.08 (step t2.t119 (cl (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))) :rule resolution :premises (t2.t111 t2.t118 a6))
% 0.90/1.08 (step t2.t120 (cl (not (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t121 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t122 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t122.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t122.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t4 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t122.t5 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t122.t6 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t122.t7 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t122.t7.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t122.t7.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t122.t7.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t122.t7.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t122.t7.t5))
% 0.90/1.08 (step t2.t122.t7.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t122.t7.t5))
% 0.90/1.08 (step t2.t122.t7.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t122.t7.t6 t2.t122.t7.t8))
% 0.90/1.08 (step t2.t122.t7.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t122.t7.t7 t2.t122.t7.t9))
% 0.90/1.08 (step t2.t122.t7.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t122.t7.t6 t2.t122.t7.t11))
% 0.90/1.08 (step t2.t122.t7.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t122.t7.t10 t2.t122.t7.t12))
% 0.90/1.08 (step t2.t122.t7.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t122.t7.t6 t2.t122.t7.t13))
% 0.90/1.08 (step t2.t122.t7.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t7.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t122.t7.t14 t2.t122.t7.t15))
% 0.90/1.08 (step t2.t122.t7 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t122.t8 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t122.t6 t2.t122.t7))
% 0.90/1.08 (step t2.t122.t9 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t122.t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t122.t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t122.t10.t5 t2.t122.t10.t6))
% 0.90/1.08 (step t2.t122.t10.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t122.t10.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t122.t10.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t122.t10.t9.t3 t2.t122.t10.t9.t4))
% 0.90/1.08 (step t2.t122.t10.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t122.t10.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t122.t10.t8 t2.t122.t10.t9))
% 0.90/1.08 (step t2.t122.t10.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t122.t10.t7 t2.t122.t10.t10))
% 0.90/1.08 (step t2.t122.t10.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t122.t10.t11 t2.t122.t10.t12))
% 0.90/1.08 (step t2.t122.t10.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t122.t10.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t122.t10.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t122.t10.t15.t2 t2.t122.t10.t15.t3))
% 0.90/1.08 (step t2.t122.t10.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t122.t10.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t122.t10.t14 t2.t122.t10.t15))
% 0.90/1.08 (step t2.t122.t10.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t122.t10.t13 t2.t122.t10.t16))
% 0.90/1.08 (step t2.t122.t10.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t122.t10.t4 t2.t122.t10.t17))
% 0.90/1.08 (step t2.t122.t10.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t122.t10.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t122.t10.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t122.t10.t20.t2))
% 0.90/1.08 (step t2.t122.t10.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t122.t10.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t122.t10.t19 t2.t122.t10.t20))
% 0.90/1.08 (step t2.t122.t10.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t122.t10.t18 t2.t122.t10.t21))
% 0.90/1.08 (step t2.t122.t10.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t10.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t122.t10.t22 t2.t122.t10.t23))
% 0.90/1.08 (step t2.t122.t10.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t122.t10.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t122.t10.t24 t2.t122.t10.t25))
% 0.90/1.08 (step t2.t122.t10 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t122.t11 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t122.t9 t2.t122.t10))
% 0.90/1.08 (step t2.t122.t12 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t122.t8 t2.t122.t11))
% 0.90/1.08 (step t2.t122.t13 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t122.t5 t2.t122.t12 a4))
% 0.90/1.08 (step t2.t122.t14 (cl (and (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t122.t4 t2.t122.t13 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t122.t15 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t122.t14))
% 0.90/1.08 (step t2.t122.t16 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t122.t14))
% 0.90/1.08 (step t2.t122.t17 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t122.t18 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t122.t16 t2.t122.t17))
% 0.90/1.08 (step t2.t122.t19 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t122.t15 t2.t122.t18))
% 0.90/1.08 (step t2.t122.t20 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t122.t21 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi))) :rule cong :premises (t2.t122.t19 t2.t122.t20))
% 0.90/1.08 (step t2.t122.t22 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t122.t23 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) :rule cong :premises (t2.t122.t21 t2.t122.t22))
% 0.90/1.08 (step t2.t122 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t123 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))))) :rule cong :premises (t2.t121 t2.t122))
% 0.90/1.08 (step t2.t124 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.90/1.08 (anchor :step t2.t125 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t125.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t125.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t125.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t125.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t125.t5 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t125.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t125.t4 t2.t125.t5))
% 0.90/1.08 (step t2.t125.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t125.t8 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t125.t8.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t125.t8.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t125.t8.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t125.t8.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t125.t8.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t125.t8.t3 t2.t125.t8.t4))
% 0.90/1.08 (step t2.t125.t8 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t125.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t125.t7 t2.t125.t8))
% 0.90/1.08 (step t2.t125.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t125.t6 t2.t125.t9))
% 0.90/1.08 (step t2.t125.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t125.t12 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi))) :rule cong :premises (t2.t125.t10 t2.t125.t11))
% 0.90/1.08 (step t2.t125.t13 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t125.t14 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t125.t12 t2.t125.t13))
% 0.90/1.08 (step t2.t125.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t125.t16 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0))) :rule cong :premises (t2.t125.t14 t2.t125.t15))
% 0.90/1.08 (step t2.t125.t17 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule all_simplify)
% 0.90/1.08 (step t2.t125.t18 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) :rule trans :premises (t2.t125.t16 t2.t125.t17))
% 0.90/1.08 (step t2.t125 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule bind)
% 0.90/1.08 (step t2.t126 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule cong :premises (t2.t124 t2.t125))
% 0.90/1.08 (step t2.t127 (cl (= (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t123 t2.t126))
% 0.90/1.08 (step t2.t128 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule resolution :premises (t2.t120 t2.t127 a5))
% 0.90/1.08 (step t2.t129 (cl (not (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) (not (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule equiv_pos2)
% 0.90/1.08 (step t2.t130 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t131 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t131.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t131.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t131.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t131.t4 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y)))) (not (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) (not (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) (not (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W))))) (not (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule and_neg)
% 0.90/1.08 (step t2.t131.t5 (cl (and (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t131.t4 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t131.t6 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t131.t5))
% 0.90/1.08 (step t2.t131.t7 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t131.t5))
% 0.90/1.08 (step t2.t131.t8 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t131.t9 (cl (= (@ tptp.mnot Phi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi))) :rule cong :premises (t2.t131.t6 t2.t131.t8))
% 0.90/1.08 (step t2.t131.t10 (cl (= (@ tptp.mor (@ tptp.mnot Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)))) :rule cong :premises (t2.t131.t7 t2.t131.t9))
% 0.90/1.08 (step t2.t131.t11 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t131.t12 (cl (= (@ tptp.mnot Psi) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) :rule cong :premises (t2.t131.t6 t2.t131.t11))
% 0.90/1.08 (step t2.t131.t13 (cl (= (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)))) :rule cong :premises (t2.t131.t10 t2.t131.t12))
% 0.90/1.08 (step t2.t131.t14 (cl (= (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))))) :rule cong :premises (t2.t131.t6 t2.t131.t13))
% 0.90/1.08 (step t2.t131.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t131.t16 (cl (= (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) :rule cong :premises (t2.t131.t14 t2.t131.t15))
% 0.90/1.08 (step t2.t131 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t132 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))))) :rule cong :premises (t2.t130 t2.t131))
% 0.90/1.08 (step t2.t133 (cl (= tptp.mand tptp.mand)) :rule refl)
% 0.90/1.08 (anchor :step t2.t134 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi) (Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t134.t1 (cl (= Phi Phi)) :rule refl)
% 0.90/1.08 (step t2.t134.t2 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t134.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t134.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t2.t134.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t2.t134.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi) (lambda ((W $$unsorted)) (not (@ Phi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t7 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))))) :rule cong :premises (t2.t134.t5 t2.t134.t6))
% 0.90/1.08 (step t2.t134.t8 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t134.t9 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t134.t9.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t2.t134.t9.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t134.t9.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (not (@ Phi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t9.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t2.t134.t9.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W)) (or (not (@ Phi W)) (@ Psi W)))) :rule cong :premises (t2.t134.t9.t3 t2.t134.t9.t4))
% 0.90/1.08 (step t2.t134.t9 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (not (@ Phi W))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule bind)
% 0.90/1.08 (step t2.t134.t10 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t134.t8 t2.t134.t9))
% 0.90/1.08 (step t2.t134.t11 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))))) :rule trans :premises (t2.t134.t7 t2.t134.t10))
% 0.90/1.08 (step t2.t134.t12 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi) (lambda ((W $$unsorted)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t13 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))))) :rule cong :premises (t2.t134.t11 t2.t134.t12))
% 0.90/1.08 (step t2.t134.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t134.t15 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t134.t15.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t134.t15.t2 (cl (= (not (@ Phi W)) (not (@ Phi W)))) :rule refl)
% 0.90/1.08 (step t2.t134.t15.t3 (cl (= (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W) (not (@ Psi W)))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t15.t4 (cl (= (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W)) (or (not (@ Phi W)) (not (@ Psi W))))) :rule cong :premises (t2.t134.t15.t2 t2.t134.t15.t3))
% 0.90/1.08 (step t2.t134.t15 (cl (= (lambda ((W $$unsorted)) (or (not (@ Phi W)) (@ (lambda ((W $$unsorted)) (not (@ Psi W))) W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule bind)
% 0.90/1.08 (step t2.t134.t16 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (not (@ Phi W)) (@ Psi W))) (lambda ((W $$unsorted)) (not (@ Psi W)))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t134.t14 t2.t134.t15))
% 0.90/1.08 (step t2.t134.t17 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi)) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))))) :rule trans :premises (t2.t134.t13 t2.t134.t16))
% 0.90/1.08 (step t2.t134.t18 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))))) :rule cong :premises (t2.t134.t4 t2.t134.t17))
% 0.90/1.08 (step t2.t134.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t134.t20 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t134.t20.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t134.t20.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W) (or (not (@ Phi W)) (not (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t20.t3 (cl (= (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W)) (not (or (not (@ Phi W)) (not (@ Psi W)))))) :rule cong :premises (t2.t134.t20.t2))
% 0.90/1.08 (step t2.t134.t20 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W)))) W))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule bind)
% 0.90/1.08 (step t2.t134.t21 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((W $$unsorted)) (or (not (@ Phi W)) (not (@ Psi W))))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t134.t19 t2.t134.t20))
% 0.90/1.08 (step t2.t134.t22 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))))) :rule trans :premises (t2.t134.t18 t2.t134.t21))
% 0.90/1.08 (step t2.t134.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t134.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0))) :rule cong :premises (t2.t134.t22 t2.t134.t23))
% 0.90/1.08 (step t2.t134.t25 (cl (= (@ (lambda ((W $$unsorted)) (not (or (not (@ Phi W)) (not (@ Psi W))))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule all_simplify)
% 0.90/1.08 (step t2.t134.t26 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) :rule trans :premises (t2.t134.t24 t2.t134.t25))
% 0.90/1.08 (step t2.t134 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0)) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule bind)
% 0.90/1.08 (step t2.t135 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Phi)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule cong :premises (t2.t133 t2.t134))
% 0.90/1.08 (step t2.t136 (cl (= (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))))) :rule trans :premises (t2.t132 t2.t135))
% 0.90/1.08 (step t2.t137 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule resolution :premises (t2.t129 t2.t136 a4))
% 0.90/1.08 (step t2.t138 (cl (and (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t69 t2.t74 t2.t83 t2.t92 a10 a9 t2.t101 t2.t110 t2.t119 t2.t128 t2.t137 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t139 (cl (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))))) :rule and :premises (t2.t138))
% 0.90/1.08 (step t2.t140 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule and :premises (t2.t138))
% 0.90/1.08 (step t2.t141 (cl (= (@ tptp.mnot tptp.mtrue) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) :rule cong :premises (t2.t139 t2.t140))
% 0.90/1.08 (step t2.t142 (cl (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))))) :rule cong :premises (t2.t68 t2.t141))
% 0.90/1.08 (step t2.t143 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.90/1.08 (step t2.t144 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t2.t145 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t2.t145.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t2.t145.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W) true)) :rule all_simplify)
% 0.90/1.08 (step t2.t145.t3 (cl (= (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) (not true))) :rule cong :premises (t2.t145.t2))
% 0.90/1.08 (step t2.t145.t4 (cl (= (not true) false)) :rule all_simplify)
% 0.90/1.08 (step t2.t145.t5 (cl (= (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) false)) :rule trans :premises (t2.t145.t3 t2.t145.t4))
% 0.90/1.08 (step t2.t145 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))) (lambda ((W $$unsorted)) false))) :rule bind)
% 0.90/1.08 (step t2.t146 (cl (= (lambda ((W $$unsorted)) false) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule all_simplify)
% 0.90/1.08 (step t2.t147 (cl (= (lambda ((W $$unsorted)) (not (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule trans :premises (t2.t145 t2.t146))
% 0.90/1.08 (step t2.t148 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule trans :premises (t2.t144 t2.t147))
% 0.90/1.08 (step t2.t149 (cl (= (= tptp.mfalse (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) :rule cong :premises (t2.t143 t2.t148))
% 0.90/1.08 (step t2.t150 (cl (= (= tptp.mfalse (@ tptp.mnot tptp.mtrue)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)))) :rule trans :premises (t2.t142 t2.t149))
% 0.90/1.08 (step t2.t151 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false))) :rule resolution :premises (t2.t67 t2.t150 a14))
% 0.90/1.08 (step t2.t152 (cl (and (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))) (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))) (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))) (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (not (forall ((V $$unsorted)) (or (not (@ (@ R T) V)) (not (@ (@ R U) V))))))))) (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))) (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (not (@ (@ R U) T))))))))) (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (or (not (@ (@ R S) T)) (not (forall ((U $$unsorted)) (or (not (@ (@ R S) U)) (= T U)))))))))) (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (= T U))))) (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U))))) (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R T) U)) (@ (@ R S) U))))) (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (not (forall ((T $$unsorted)) (not (@ (@ R S) T))))))) (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (or (not (@ (@ R S) T)) (@ (@ R T) S))))) (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (not (@ Phi V))))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_4863 $$unsorted)) false)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((P (-> $$unsorted Bool))) (not (@ (@ Phi P) __flatten_var_0)))))) (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((X tptp.mu)) (not (@ (@ Phi X) __flatten_var_0)))))) (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))) (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))) (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))))) (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (not (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0))))))) (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Psi __flatten_var_0)) (@ Phi __flatten_var_0)))) (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0)))) (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0)))))) (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))) (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))) (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))) (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) :rule resolution :premises (t2.t2 t2.t7 t2.t12 a28 a27 t2.t17 t2.t22 t2.t27 t2.t32 t2.t37 t2.t42 t2.t47 t2.t52 t2.t57 a17 t2.t66 a15 t2.t151 t2.t74 t2.t83 t2.t92 a10 a9 t2.t101 t2.t110 t2.t119 t2.t128 t2.t137 a3 a2 a1 a0))
% 0.90/1.08 (step t2.t153 (cl (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t154 (cl (= R R)) :rule refl)
% 0.90/1.08 (step t2.t155 (cl (= (@ tptp.mweakly_connected R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R))) :rule cong :premises (t2.t153 t2.t154))
% 0.90/1.08 (step t2.t156 (cl (= (not (@ tptp.mweakly_connected R)) (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)))) :rule cong :premises (t2.t155))
% 0.90/1.08 (step t2.t157 (cl (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t158 (cl (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule and :premises (t2.t152))
% 0.90/1.08 (anchor :step t2.t159 :args ((A (-> $$unsorted Bool)) (:= A A) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t159.t1 (cl (= A A)) :rule refl)
% 0.90/1.08 (step t2.t159.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (anchor :step t2.t159.t3 :args ((B (-> $$unsorted Bool)) (:= B B) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t2.t159.t3.t1 (cl (= B B)) :rule refl)
% 0.90/1.08 (step t2.t159.t3.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t159.t3.t3 (cl (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t159.t3.t4 (cl (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t159.t3.t5 (cl (= (@ tptp.mbox R) (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R))) :rule cong :premises (t2.t159.t3.t4 t2.t154))
% 0.90/1.08 (step t2.t159.t3.t6 (cl (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t159.t3.t7 (cl (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule and :premises (t2.t152))
% 0.90/1.08 (step t2.t159.t3.t8 (cl (= A A)) :rule refl)
% 0.90/1.08 (step t2.t159.t3.t9 (cl (= (@ tptp.mand A) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A))) :rule cong :premises (t2.t159.t3.t7 t2.t159.t3.t8))
% 0.90/1.08 (step t2.t159.t3.t10 (cl (= (@ (@ tptp.mbox R) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) :rule cong :premises (t2.t159.t3.t5 t2.t159.t3.t8))
% 0.90/1.08 (step t2.t159.t3.t11 (cl (= (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A)))) :rule cong :premises (t2.t159.t3.t9 t2.t159.t3.t10))
% 0.90/1.08 (step t2.t159.t3.t12 (cl (= (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))))) :rule cong :premises (t2.t159.t3.t6 t2.t159.t3.t11))
% 0.90/1.08 (step t2.t159.t3.t13 (cl (= B B)) :rule refl)
% 0.90/1.08 (step t2.t159.t3.t14 (cl (= (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) :rule cong :premises (t2.t159.t3.t12 t2.t159.t3.t13))
% 0.90/1.08 (step t2.t159.t3.t15 (cl (= (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B)))) :rule cong :premises (t2.t159.t3.t5 t2.t159.t3.t14))
% 0.90/1.08 (step t2.t159.t3.t16 (cl (= (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))))) :rule cong :premises (t2.t159.t3.t3 t2.t159.t3.t15))
% 0.90/1.08 (step t2.t159.t3.t17 (cl (= (@ tptp.mand B) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B))) :rule cong :premises (t2.t159.t3.t7 t2.t159.t3.t13))
% 0.90/1.08 (step t2.t159.t3.t18 (cl (= (@ (@ tptp.mbox R) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) :rule cong :premises (t2.t159.t3.t5 t2.t159.t3.t13))
% 0.90/1.08 (step t2.t159.t3.t19 (cl (= (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B)) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B)))) :rule cong :premises (t2.t159.t3.t17 t2.t159.t3.t18))
% 0.90/1.08 (step t2.t159.t3.t20 (cl (= (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))))) :rule cong :premises (t2.t159.t3.t6 t2.t159.t3.t19))
% 0.90/1.08 (step t2.t159.t3.t21 (cl (= (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) :rule cong :premises (t2.t159.t3.t20 t2.t159.t3.t8))
% 0.90/1.08 (step t2.t159.t3.t22 (cl (= (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A)))) :rule cong :premises (t2.t159.t3.t5 t2.t159.t3.t21))
% 0.90/1.08 (step t2.t159.t3.t23 (cl (= (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))))) :rule cong :premises (t2.t159.t3.t16 t2.t159.t3.t22))
% 0.90/1.08 (step t2.t159.t3.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t159.t3.t25 (cl (= (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) :rule cong :premises (t2.t159.t3.t23 t2.t159.t3.t24))
% 0.90/1.08 (step t2.t159.t3 (cl (= (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0)) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t159.t4 (cl (= (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))))) :rule cong :premises (t2.t158 t2.t159.t3))
% 0.90/1.08 (step t2.t159.t5 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t2.t159.t6 (cl (= (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))) :rule cong :premises (t2.t159.t4 t2.t159.t5))
% 0.90/1.08 (step t2.t159 (cl (= (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))) :rule bind)
% 0.90/1.08 (step t2.t160 (cl (= (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))) :rule cong :premises (t2.t158 t2.t159))
% 0.90/1.08 (step t2.t161 (cl (= (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))))) :rule cong :premises (t2.t157 t2.t160))
% 0.90/1.08 (step t2.t162 (cl (= (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) :rule cong :premises (t2.t156 t2.t161))
% 0.90/1.08 (step t2 (cl (= (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))) (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) :rule bind)
% 0.90/1.08 (step t3 (cl (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))))))) :rule cong :premises (t2))
% 0.90/1.08 (anchor :step t4 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R)))
% 0.90/1.08 (step t4.t1 (cl (= R R)) :rule refl)
% 0.90/1.08 (step t4.t2 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T))))) :rule all_simplify)
% 0.90/1.08 (step t4.t3 (cl (= (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (not (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))))) :rule cong :premises (t4.t2))
% 0.90/1.08 (step t4.t4 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) :rule refl)
% 0.90/1.08 (step t4.t5 (cl (= (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))))) :rule refl)
% 0.90/1.08 (anchor :step t4.t6 :args ((A (-> $$unsorted Bool)) (:= A A) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t1 (cl (= A A)) :rule refl)
% 0.90/1.08 (step t4.t6.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (anchor :step t4.t6.t3 :args ((B (-> $$unsorted Bool)) (:= B B) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t3.t1 (cl (= B B)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t3 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t4 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t5 (cl (= (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t6 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t7 (cl (= A A)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t8 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) A))) :rule cong :premises (t4.t6.t3.t4 t4.t6.t3.t7))
% 0.90/1.08 (step t4.t6.t3.t9 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) A) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t10 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))))) :rule trans :premises (t4.t6.t3.t8 t4.t6.t3.t9))
% 0.90/1.08 (step t4.t6.t3.t11 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V))))))) :rule cong :premises (t4.t6.t3.t6 t4.t6.t3.t10))
% 0.90/1.08 (step t4.t6.t3.t12 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t13 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t3.t13.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t13.t2 (cl (= (not (@ A __flatten_var_0)) (not (@ A __flatten_var_0)))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t13.t3 (cl (= (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t13.t4 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) :rule cong :premises (t4.t6.t3.t13.t3))
% 0.90/1.08 (step t4.t6.t3.t13.t5 (cl (= (or (not (@ A __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0))) (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) :rule cong :premises (t4.t6.t3.t13.t2 t4.t6.t3.t13.t4))
% 0.90/1.08 (step t4.t6.t3.t13.t6 (cl (= (not (or (not (@ A __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0)))) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule cong :premises (t4.t6.t3.t13.t5))
% 0.90/1.08 (step t4.t6.t3.t13 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V)))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t14 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))))) :rule trans :premises (t4.t6.t3.t12 t4.t6.t3.t13))
% 0.90/1.08 (step t4.t6.t3.t15 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))))) :rule trans :premises (t4.t6.t3.t11 t4.t6.t3.t14))
% 0.90/1.08 (step t4.t6.t3.t16 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))))) :rule cong :premises (t4.t6.t3.t5 t4.t6.t3.t15))
% 0.90/1.08 (step t4.t6.t3.t17 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t18 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t3.t18.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t18.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t18.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (not (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))))) :rule cong :premises (t4.t6.t3.t18.t3))
% 0.90/1.08 (step t4.t6.t3.t18.t5 (cl (= (not (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t18.t6 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) :rule trans :premises (t4.t6.t3.t18.t4 t4.t6.t3.t18.t5))
% 0.90/1.08 (step t4.t6.t3.t18.t7 (cl (= (@ Psi __flatten_var_0) (@ Psi __flatten_var_0))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t18.t8 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (@ Psi __flatten_var_0)) (or (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))) (@ Psi __flatten_var_0)))) :rule cong :premises (t4.t6.t3.t18.t6 t4.t6.t3.t18.t7))
% 0.90/1.08 (step t4.t6.t3.t18.t9 (cl (= (or (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))) (@ Psi __flatten_var_0)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t18.t10 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (@ Psi __flatten_var_0)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) :rule trans :premises (t4.t6.t3.t18.t8 t4.t6.t3.t18.t9))
% 0.90/1.08 (step t4.t6.t3.t18 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule trans :premises (t4.t6.t3.t17 t4.t6.t3.t18))
% 0.90/1.08 (step t4.t6.t3.t20 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule trans :premises (t4.t6.t3.t16 t4.t6.t3.t19))
% 0.90/1.08 (step t4.t6.t3.t21 (cl (= B B)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t22 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) B))) :rule cong :premises (t4.t6.t3.t20 t4.t6.t3.t21))
% 0.90/1.08 (step t4.t6.t3.t23 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) B) (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t24 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B) (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))))) :rule trans :premises (t4.t6.t3.t22 t4.t6.t3.t23))
% 0.90/1.08 (step t4.t6.t3.t25 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))))) :rule cong :premises (t4.t6.t3.t4 t4.t6.t3.t24))
% 0.90/1.08 (step t4.t6.t3.t26 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V)))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t27 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t6.t3.t27.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (anchor :step t4.t6.t3.t27.t2 :args ((V $$unsorted) (:= V V)))
% 0.90/1.08 (step t4.t6.t3.t27.t2.t1 (cl (= V V)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t27.t2.t2 (cl (= (not (@ (@ R W) V)) (not (@ (@ R W) V)))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t27.t2.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V) (or (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t27.t2.t4 (cl (= (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V)) (or (not (@ (@ R W) V)) (or (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V)))))))) :rule cong :premises (t4.t6.t3.t27.t2.t2 t4.t6.t3.t27.t2.t3))
% 0.90/1.08 (step t4.t6.t3.t27.t2.t5 (cl (= (or (not (@ (@ R W) V)) (or (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V)))))) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t27.t2.t6 (cl (= (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V))))))) :rule trans :premises (t4.t6.t3.t27.t2.t4 t4.t6.t3.t27.t2.t5))
% 0.90/1.08 (step t4.t6.t3.t27.t2 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t27.t3 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V)))))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t27.t4 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t27.t5 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ A V)))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule trans :premises (t4.t6.t3.t27.t3 t4.t6.t3.t27.t4))
% 0.90/1.08 (step t4.t6.t3.t27.t6 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule trans :premises (t4.t6.t3.t27.t2 t4.t6.t3.t27.t5))
% 0.90/1.08 (step t4.t6.t3.t27 (cl (= (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V)))))) V)))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t28 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ B __flatten_var_0) (not (@ A __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V))))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule trans :premises (t4.t6.t3.t26 t4.t6.t3.t27))
% 0.90/1.08 (step t4.t6.t3.t29 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B)) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule trans :premises (t4.t6.t3.t25 t4.t6.t3.t28))
% 0.90/1.08 (step t4.t6.t3.t30 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))))) :rule cong :premises (t4.t6.t3.t3 t4.t6.t3.t29))
% 0.90/1.08 (step t4.t6.t3.t31 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) W) (@ Psi W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t32 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t6.t3.t32.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t32.t2 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t32.t3 (cl (= (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) W) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t32.t4 (cl (= (@ Psi W) (@ Psi W))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t32.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) W) (@ Psi W)) (or (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))) (@ Psi W)))) :rule cong :premises (t4.t6.t3.t32.t3 t4.t6.t3.t32.t4))
% 0.90/1.08 (step t4.t6.t3.t32.t6 (cl (= (or (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))) (@ Psi W)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t32.t7 (cl (= (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) W) (@ Psi W)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule trans :premises (t4.t6.t3.t32.t5 t4.t6.t3.t32.t6))
% 0.90/1.08 (step t4.t6.t3.t32 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) W) (@ Psi W))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t33 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule trans :premises (t4.t6.t3.t31 t4.t6.t3.t32))
% 0.90/1.08 (step t4.t6.t3.t34 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule trans :premises (t4.t6.t3.t30 t4.t6.t3.t33))
% 0.90/1.08 (step t4.t6.t3.t35 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ Psi __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t36 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) B))) :rule cong :premises (t4.t6.t3.t4 t4.t6.t3.t21))
% 0.90/1.08 (step t4.t6.t3.t37 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) B) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t38 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))))) :rule trans :premises (t4.t6.t3.t36 t4.t6.t3.t37))
% 0.90/1.08 (step t4.t6.t3.t39 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B)) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V))))))) :rule cong :premises (t4.t6.t3.t35 t4.t6.t3.t38))
% 0.90/1.08 (step t4.t6.t3.t40 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t41 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t3.t41.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t41.t2 (cl (= (not (@ B __flatten_var_0)) (not (@ B __flatten_var_0)))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t41.t3 (cl (= (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t41.t4 (cl (= (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) :rule cong :premises (t4.t6.t3.t41.t3))
% 0.90/1.08 (step t4.t6.t3.t41.t5 (cl (= (or (not (@ B __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0))) (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) :rule cong :premises (t4.t6.t3.t41.t2 t4.t6.t3.t41.t4))
% 0.90/1.08 (step t4.t6.t3.t41.t6 (cl (= (not (or (not (@ B __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0)))) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule cong :premises (t4.t6.t3.t41.t5))
% 0.90/1.08 (step t4.t6.t3.t41 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V)))) __flatten_var_0))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t42 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (@ Psi __flatten_var_0))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))))) :rule trans :premises (t4.t6.t3.t40 t4.t6.t3.t41))
% 0.90/1.08 (step t4.t6.t3.t43 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))))) :rule trans :premises (t4.t6.t3.t39 t4.t6.t3.t42))
% 0.90/1.08 (step t4.t6.t3.t44 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))))) :rule cong :premises (t4.t6.t3.t5 t4.t6.t3.t43))
% 0.90/1.08 (step t4.t6.t3.t45 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (@ Psi __flatten_var_0))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t46 :args ((Psi (-> $$unsorted Bool)) (:= Psi Psi) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t6.t3.t46.t1 (cl (= Psi Psi)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t46.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t46.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t46.t4 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (not (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))))) :rule cong :premises (t4.t6.t3.t46.t3))
% 0.90/1.08 (step t4.t6.t3.t46.t5 (cl (= (not (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t46.t6 (cl (= (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) :rule trans :premises (t4.t6.t3.t46.t4 t4.t6.t3.t46.t5))
% 0.90/1.08 (step t4.t6.t3.t46.t7 (cl (= (@ Psi __flatten_var_0) (@ Psi __flatten_var_0))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t46.t8 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (@ Psi __flatten_var_0)) (or (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))) (@ Psi __flatten_var_0)))) :rule cong :premises (t4.t6.t3.t46.t6 t4.t6.t3.t46.t7))
% 0.90/1.08 (step t4.t6.t3.t46.t9 (cl (= (or (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))) (@ Psi __flatten_var_0)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t46.t10 (cl (= (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (@ Psi __flatten_var_0)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) :rule trans :premises (t4.t6.t3.t46.t8 t4.t6.t3.t46.t9))
% 0.90/1.08 (step t4.t6.t3.t46 (cl (= (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t47 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule trans :premises (t4.t6.t3.t45 t4.t6.t3.t46))
% 0.90/1.08 (step t4.t6.t3.t48 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule trans :premises (t4.t6.t3.t44 t4.t6.t3.t47))
% 0.90/1.08 (step t4.t6.t3.t49 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A) (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) A))) :rule cong :premises (t4.t6.t3.t48 t4.t6.t3.t7))
% 0.90/1.08 (step t4.t6.t3.t50 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (@ Psi __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) A) (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t51 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A) (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))))) :rule trans :premises (t4.t6.t3.t49 t4.t6.t3.t50))
% 0.90/1.08 (step t4.t6.t3.t52 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A)) (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))))) :rule cong :premises (t4.t6.t3.t4 t4.t6.t3.t51))
% 0.90/1.08 (step t4.t6.t3.t53 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V)))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t54 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t6.t3.t54.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (anchor :step t4.t6.t3.t54.t2 :args ((V $$unsorted) (:= V V)))
% 0.90/1.08 (step t4.t6.t3.t54.t2.t1 (cl (= V V)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t54.t2.t2 (cl (= (not (@ (@ R W) V)) (not (@ (@ R W) V)))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t54.t2.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V) (or (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t54.t2.t4 (cl (= (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V)) (or (not (@ (@ R W) V)) (or (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V)))))))) :rule cong :premises (t4.t6.t3.t54.t2.t2 t4.t6.t3.t54.t2.t3))
% 0.90/1.08 (step t4.t6.t3.t54.t2.t5 (cl (= (or (not (@ (@ R W) V)) (or (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V)))))) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t54.t2.t6 (cl (= (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V))))))) :rule trans :premises (t4.t6.t3.t54.t2.t4 t4.t6.t3.t54.t2.t5))
% 0.90/1.08 (step t4.t6.t3.t54.t2 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t54.t3 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V)))))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t54.t4 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))))) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t54.t5 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)) (not (forall ((V $$unsorted)) (or (not (@ (@ R V) V)) (@ B V)))))) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule trans :premises (t4.t6.t3.t54.t3 t4.t6.t3.t54.t4))
% 0.90/1.08 (step t4.t6.t3.t54.t6 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V))) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule trans :premises (t4.t6.t3.t54.t2 t4.t6.t3.t54.t5))
% 0.90/1.08 (step t4.t6.t3.t54 (cl (= (lambda ((W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V)))))) V)))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t55 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) (lambda ((__flatten_var_0 $$unsorted)) (or (@ A __flatten_var_0) (not (@ B __flatten_var_0)) (not (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V))))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule trans :premises (t4.t6.t3.t53 t4.t6.t3.t54))
% 0.90/1.08 (step t4.t6.t3.t56 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A)) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule trans :premises (t4.t6.t3.t52 t4.t6.t3.t55))
% 0.90/1.08 (step t4.t6.t3.t57 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))))) :rule cong :premises (t4.t6.t3.t34 t4.t6.t3.t56))
% 0.90/1.08 (step t4.t6.t3.t58 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) (lambda ((W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t3.t59 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t6.t3.t59.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t59.t2 (cl (= (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) W) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t59.t3 (cl (= (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t59.t4 (cl (= (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t59.t5 (cl (= (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))) (or (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))))) :rule cong :premises (t4.t6.t3.t59.t2 t4.t6.t3.t59.t3 t4.t6.t3.t59.t4))
% 0.90/1.08 (step t4.t6.t3.t59.t6 (cl (= (or (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t59.t7 (cl (= (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) :rule trans :premises (t4.t6.t3.t59.t5 t4.t6.t3.t59.t6))
% 0.90/1.08 (step t4.t6.t3.t59 (cl (= (lambda ((W $$unsorted)) (or (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t3.t60 (cl (= (@ (lambda ((Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Psi W) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V))))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule trans :premises (t4.t6.t3.t58 t4.t6.t3.t59))
% 0.90/1.08 (step t4.t6.t3.t61 (cl (= (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))))) :rule trans :premises (t4.t6.t3.t57 t4.t6.t3.t60))
% 0.90/1.08 (step t4.t6.t3.t62 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t3.t63 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) __flatten_var_0))) :rule cong :premises (t4.t6.t3.t61 t4.t6.t3.t62))
% 0.90/1.08 (step t4.t6.t3.t64 (cl (= (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ B V)))))) __flatten_var_0) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t3.t65 (cl (= (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V))))))) :rule trans :premises (t4.t6.t3.t63 t4.t6.t3.t64))
% 0.90/1.08 (step t4.t6.t3 (cl (= (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0)) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t4 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V))))))))) :rule cong :premises (t4.t5 t4.t6.t3))
% 0.90/1.08 (step t4.t6.t5 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V))))))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t6 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t6.t6.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (anchor :step t4.t6.t6.t2 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.90/1.08 (step t4.t6.t6.t2.t1 (cl (= P P)) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t2.t2 (cl (= (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ P V)))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t6.t2.t3 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t2.t4 (cl (= (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ P V)))))) W))) :rule cong :premises (t4.t6.t6.t2.t2 t4.t6.t6.t2.t3))
% 0.90/1.08 (step t4.t6.t6.t2.t5 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ P V)))))) W) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t6.t2.t6 (cl (= (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V))))))) :rule trans :premises (t4.t6.t6.t2.t4 t4.t6.t6.t2.t5))
% 0.90/1.08 (step t4.t6.t6.t2 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W)) (forall ((P (-> $$unsorted Bool))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t6.t3 (cl (= (forall ((P (-> $$unsorted Bool))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V)))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool))) (or (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V))))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t6.t4 (cl (= (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))))) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t5 (cl (= (forall ((P (-> $$unsorted Bool))) (or (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V)))))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (or (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (or (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t6.t6.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (BOUND_VARIABLE_1859 $$unsorted) (:= BOUND_VARIABLE_1859 BOUND_VARIABLE_1859) (BOUND_VARIABLE_1851 $$unsorted) (:= BOUND_VARIABLE_1851 BOUND_VARIABLE_1851)))
% 0.90/1.08 (step t4.t6.t6.t6.t1 (cl (= P P)) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t6.t2 (cl (= BOUND_VARIABLE_1859 BOUND_VARIABLE_1859)) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t6.t3 (cl (= BOUND_VARIABLE_1851 BOUND_VARIABLE_1851)) :rule refl)
% 0.90/1.08 (step t4.t6.t6.t6.t4 (cl (= (or (or (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (or (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t6.t6 (cl (= (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (or (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (or (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) :rule bind)
% 0.90/1.08 (step t4.t6.t6.t7 (cl (= (forall ((P (-> $$unsorted Bool))) (or (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V)))))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) :rule trans :premises (t4.t6.t6.t5 t4.t6.t6.t6))
% 0.90/1.08 (step t4.t6.t6.t8 (cl (= (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool))) (or (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V))))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule cong :premises (t4.t6.t6.t4 t4.t6.t6.t7))
% 0.90/1.08 (step t4.t6.t6.t9 (cl (= (forall ((P (-> $$unsorted Bool))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ P V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ A V) (not (@ P V)))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule trans :premises (t4.t6.t6.t3 t4.t6.t6.t8))
% 0.90/1.08 (step t4.t6.t6.t10 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule trans :premises (t4.t6.t6.t2 t4.t6.t6.t9))
% 0.90/1.08 (step t4.t6.t6 (cl (= (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V)))))) P) W))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))))) :rule bind)
% 0.90/1.08 (step t4.t6.t7 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ B V) (not (@ A V)))) (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ B BOUND_VARIABLE_1780)))) (forall ((V $$unsorted)) (or (not (@ (@ R __flatten_var_0) V)) (@ A V) (not (@ B V))))))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))))) :rule trans :premises (t4.t6.t5 t4.t6.t6))
% 0.90/1.08 (step t4.t6.t8 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))))) :rule trans :premises (t4.t6.t4 t4.t6.t7))
% 0.90/1.08 (step t4.t6.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t6.t10 (cl (= (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0) (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) __flatten_var_0))) :rule cong :premises (t4.t6.t8 t4.t6.t9))
% 0.90/1.08 (step t4.t6.t11 (cl (= (@ (lambda ((W $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R W) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R W) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) __flatten_var_0) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule all_simplify)
% 0.90/1.08 (step t4.t6.t12 (cl (= (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) :rule trans :premises (t4.t6.t10 t4.t6.t11))
% 0.90/1.08 (step t4.t6 (cl (= (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))))) :rule bind)
% 0.90/1.08 (step t4.t7 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))))) :rule cong :premises (t4.t5 t4.t6))
% 0.90/1.08 (step t4.t8 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t9 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t9.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (anchor :step t4.t9.t2 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.90/1.08 (step t4.t9.t2.t1 (cl (= P P)) :rule refl)
% 0.90/1.08 (step t4.t9.t2.t2 (cl (= (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t9.t2.t3 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.90/1.08 (step t4.t9.t2.t3.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.90/1.08 (step t4.t9.t2.t3.t2 (cl (= (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))))) :rule refl)
% 0.90/1.08 (step t4.t9.t2.t3.t3 (cl (= (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) true))) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t2.t3.t4 (cl (= (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) true) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t2.t3.t5 (cl (= (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))) true)) :rule trans :premises (t4.t9.t2.t3.t3 t4.t9.t2.t3.t4))
% 0.90/1.08 (step t4.t9.t2.t3.t6 (cl (= (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) true))) :rule cong :premises (t4.t9.t2.t3.t2 t4.t9.t2.t3.t5))
% 0.90/1.08 (step t4.t9.t2.t3.t7 (cl (= (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) true) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t2.t3.t8 (cl (= (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))) true)) :rule trans :premises (t4.t9.t2.t3.t6 t4.t9.t2.t3.t7))
% 0.90/1.08 (step t4.t9.t2.t3 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) (lambda ((__flatten_var_0 $$unsorted)) true))) :rule bind)
% 0.90/1.08 (step t4.t9.t2.t4 (cl (= (lambda ((__flatten_var_0 $$unsorted)) true) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t2.t5 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ P BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ P BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ P BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule trans :premises (t4.t9.t2.t3 t4.t9.t2.t4))
% 0.90/1.08 (step t4.t9.t2.t6 (cl (= (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule trans :premises (t4.t9.t2.t2 t4.t9.t2.t5))
% 0.90/1.08 (step t4.t9.t2.t7 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t4.t9.t2.t8 (cl (= (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W) (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W))) :rule cong :premises (t4.t9.t2.t6 t4.t9.t2.t7))
% 0.90/1.08 (step t4.t9.t2.t9 (cl (= (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t2.t10 (cl (= (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W) true)) :rule trans :premises (t4.t9.t2.t8 t4.t9.t2.t9))
% 0.90/1.08 (step t4.t9.t2 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W)) (forall ((P (-> $$unsorted Bool))) true))) :rule bind)
% 0.90/1.08 (step t4.t9.t3 (cl (= (forall ((P (-> $$unsorted Bool))) true) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t9.t4 (cl (= (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W)) true)) :rule trans :premises (t4.t9.t2 t4.t9.t3))
% 0.90/1.08 (step t4.t9 (cl (= (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W))) (lambda ((W $$unsorted)) true))) :rule bind)
% 0.90/1.08 (step t4.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule all_simplify)
% 0.90/1.08 (step t4.t11 (cl (= (lambda ((W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859)))))) P) W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule trans :premises (t4.t9 t4.t10))
% 0.90/1.08 (step t4.t12 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1697 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1697) BOUND_VARIABLE_1697)) (@ A BOUND_VARIABLE_1697)))) (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_1859 $$unsorted) (BOUND_VARIABLE_1851 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_1780 $$unsorted)) (or (not (@ (@ R BOUND_VARIABLE_1780) BOUND_VARIABLE_1780)) (@ P BOUND_VARIABLE_1780)))) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1851)) (@ P BOUND_VARIABLE_1851) (not (@ A BOUND_VARIABLE_1851)) (not (@ (@ R __flatten_var_0) BOUND_VARIABLE_1859)) (@ A BOUND_VARIABLE_1859) (not (@ P BOUND_VARIABLE_1859))))))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule trans :premises (t4.t8 t4.t11))
% 0.90/1.08 (step t4.t13 (cl (= (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true))) :rule trans :premises (t4.t7 t4.t12))
% 0.90/1.08 (step t4.t14 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)))) :rule cong :premises (t4.t4 t4.t13))
% 0.90/1.08 (step t4.t15 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) (forall ((W $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)))) :rule all_simplify)
% 0.90/1.08 (anchor :step t4.t16 :args ((W $$unsorted) (:= W W)))
% 0.90/1.08 (step t4.t16.t1 (cl (= W W)) :rule refl)
% 0.90/1.08 (step t4.t16.t2 (cl (= (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t16 (cl (= (forall ((W $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) (forall ((W $$unsorted)) true))) :rule bind)
% 0.90/1.08 (step t4.t17 (cl (= (forall ((W $$unsorted)) true) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t18 (cl (= (forall ((W $$unsorted)) (@ (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true) W)) true)) :rule trans :premises (t4.t16 t4.t17))
% 0.90/1.08 (step t4.t19 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((BOUND_VARIABLE_1527 $$unsorted)) true)) true)) :rule trans :premises (t4.t15 t4.t18))
% 0.90/1.08 (step t4.t20 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))) true)) :rule trans :premises (t4.t14 t4.t19))
% 0.90/1.08 (step t4.t21 (cl (= (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))) (or (not (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) true))) :rule cong :premises (t4.t3 t4.t20))
% 0.90/1.08 (step t4.t22 (cl (= (or (not (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) true) true)) :rule all_simplify)
% 0.90/1.08 (step t4.t23 (cl (= (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))) true)) :rule trans :premises (t4.t21 t4.t22))
% 0.90/1.08 (step t4 (cl (= (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))))) (forall ((R (-> $$unsorted $$unsorted Bool))) true))) :rule bind)
% 0.90/1.08 (step t5 (cl (= (forall ((R (-> $$unsorted $$unsorted Bool))) true) true)) :rule all_simplify)
% 0.90/1.08 (step t6 (cl (= (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0)))))) true)) :rule trans :premises (t4 t5))
% 0.90/1.08 (step t7 (cl (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) (not true))) :rule cong :premises (t6))
% 0.90/1.08 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.90/1.08 (step t9 (cl (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (or (not (@ (@ R S) T)) (not (@ (@ R S) U)) (@ (@ R T) U) (= T U) (@ (@ R U) T)))) R)) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W))) (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) A) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) A))) B))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ Phi __flatten_var_0)) (@ Psi __flatten_var_0))) (@ (@ (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (not (@ Phi __flatten_var_0)) (not (@ Psi __flatten_var_0))))) B) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V)))) R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) false)) :rule trans :premises (t7 t8))
% 0.90/1.08 (step t10 (cl (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) false)) :rule trans :premises (t3 t9))
% 0.90/1.08 (step t11 (cl (not (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ tptp.mweakly_connected R) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))))) (not (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ tptp.mweakly_connected R) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) :rule equiv_pos2)
% 0.90/1.08 (step t12 (cl (= (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ tptp.mweakly_connected R) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))) (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) :rule all_simplify)
% 0.90/1.08 (step t13 (cl (= (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ tptp.mweakly_connected R) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))) (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0))))))))) :rule cong :premises (t12))
% 0.90/1.08 (step t14 (cl (not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ tptp.mweakly_connected R)) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_prop (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand A) (@ (@ tptp.mbox R) A))) B))) (@ (@ tptp.mbox R) (@ (@ tptp.mimplies (@ (@ tptp.mand B) (@ (@ tptp.mbox R) B))) A))) __flatten_var_0))) __flatten_var_0)))))))) :rule resolution :premises (t11 t13 a31))
% 0.90/1.08 (step t15 (cl false) :rule resolution :premises (t1 t10 t14))
% 0.90/1.08 (step t16 (cl (not false)) :rule false)
% 0.90/1.08 (step t17 (cl) :rule resolution :premises (t15 t16))
% 0.90/1.08
% 0.90/1.08 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.jICiHzm6Hm/cvc5---1.0.5_15428.smt2
% 0.90/1.09 % cvc5---1.0.5 exiting
% 0.90/1.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------