%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP209_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:12:48 EDT 2024

% Result   : Theorem 0.41s 0.58s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : ITP209_1 : TPTP v8.2.0. Released v8.0.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.39  % Computer : n009.cluster.edu
% 0.16/0.39  % Model    : x86_64 x86_64
% 0.16/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39  % Memory   : 8042.1875MB
% 0.16/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39  % CPULimit   : 300
% 0.16/0.39  % WCLimit    : 300
% 0.16/0.39  % DateTime   : Sun May 26 02:51:09 EDT 2024
% 0.16/0.39  % CPUTime    : 
% 0.26/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.41/0.58  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.41/0.58  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.WXGljJ12Jm/cvc5---1.0.5_31519.smt2
% 0.41/0.58  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.WXGljJ12Jm/cvc5---1.0.5_31519.smt2
% 0.41/0.58  (assume a0 (tptp.syntax_ac_operator_a tptp.f))
% 0.41/0.58  (assume a1 (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))))
% 0.41/0.58  (assume a2 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))))
% 0.41/0.58  (assume a3 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))))
% 0.41/0.58  (assume a4 (forall ((F tptp.fun_a_fun_a_a)) (=> (forall ((A2 tptp.a) (B2 tptp.a) (C2 tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F (tptp.aa_a_a (tptp.aa_a_fun_a_a F A2) B2)) C2) (tptp.aa_a_a (tptp.aa_a_fun_a_a F A2) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B2) C2)))) (=> (forall ((A2 tptp.a) (B2 tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F A2) B2) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B2) A2))) (tptp.syntax_ac_operator_a F)))))
% 0.41/0.58  (assume a5 (forall ((F tptp.fun_a_fun_a_a) (A tptp.a) (B tptp.a)) (=> (tptp.syntax_ac_operator_a F) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B) A)))))
% 0.41/0.58  (assume a6 (forall ((F tptp.fun_a_fun_a_a) (A tptp.a) (B tptp.a) (C tptp.a)) (=> (tptp.syntax_ac_operator_a F) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a F (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) B)) C)))))
% 0.41/0.58  (assume a7 (forall ((F tptp.fun_a_fun_a_a) (A tptp.a) (B tptp.a) (C tptp.a)) (=> (tptp.syntax_ac_operator_a F) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B) C))))))
% 0.41/0.58  (assume a8 (forall ((F tptp.fun_a_fun_a_a) (A tptp.a) (B tptp.a) (C tptp.a)) (=> (tptp.syntax_ac_operator_a F) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B) (tptp.aa_a_a (tptp.aa_a_fun_a_a F A) C))))))
% 0.41/0.58  (assume a9 (forall ((F tptp.fun_a_fun_a_a)) (= (tptp.syntax_ac_operator_a F) (and (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F (tptp.aa_a_a (tptp.aa_a_fun_a_a F A3) B3)) C3) (tptp.aa_a_a (tptp.aa_a_fun_a_a F A3) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B3) C3)))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a F A3) B3) (tptp.aa_a_a (tptp.aa_a_fun_a_a F B3) A3)))))))
% 0.41/0.58  (assume a10 (tptp.pp tptp.fTrue))
% 0.41/0.58  (assume a11 (not (tptp.pp tptp.fFalse)))
% 0.41/0.58  (assume a12 (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))
% 0.41/0.58  (assume a13 true)
% 0.41/0.58  (step t1 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C))))) :rule implies_neg1)
% 0.41/0.58  (anchor :step t2)
% 0.41/0.58  (assume t2.a0 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))))
% 0.41/0.58  (step t2.t1 (cl (or (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule forall_inst :args ((:= A tptp.b) (:= B tptp.a2) (:= C tptp.c)))
% 0.41/0.58  (step t2.t2 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule or :premises (t2.t1))
% 0.41/0.58  (step t2.t3 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule resolution :premises (t2.t2 t2.a0))
% 0.41/0.58  (step t2 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule subproof :discharge (t2.a0))
% 0.41/0.58  (step t3 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule resolution :premises (t1 t2))
% 0.41/0.58  (step t4 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule implies_neg2)
% 0.41/0.58  (step t5 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t3 t4))
% 0.41/0.58  (step t6 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule contraction :premises (t5))
% 0.41/0.58  (step t7 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule implies :premises (t6))
% 0.41/0.58  (step t8 (cl (not (= (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (or (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))))) (not (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) (or (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule equiv_pos2)
% 0.41/0.58  (step t9 (cl (= (= (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) true) (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) :rule equiv_simplify)
% 0.41/0.58  (step t10 (cl (not (= (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) true)) (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule equiv1 :premises (t9))
% 0.41/0.58  (step t11 (cl (= (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))))) :rule all_simplify)
% 0.41/0.58  (step t12 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule refl)
% 0.41/0.58  (step t13 (cl (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule all_simplify)
% 0.41/0.58  (step t14 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) :rule cong :premises (t12 t13))
% 0.41/0.58  (step t15 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) true)) :rule all_simplify)
% 0.41/0.58  (step t16 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) true)) :rule trans :premises (t14 t15))
% 0.41/0.58  (step t17 (cl (= (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) true)) :rule trans :premises (t11 t16))
% 0.41/0.58  (step t18 (cl (= (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule resolution :premises (t10 t17))
% 0.41/0.58  (step t19 (cl (= (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))))) :rule refl)
% 0.41/0.58  (step t20 (cl (= (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule refl)
% 0.41/0.58  (step t21 (cl (= (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule refl)
% 0.41/0.58  (step t22 (cl (= (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (or (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))))) :rule cong :premises (t18 t19 t20 t21))
% 0.41/0.58  (step t23 (cl (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule and_neg)
% 0.41/0.58  (step t24 (cl (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule implies_neg1)
% 0.41/0.58  (anchor :step t25)
% 0.41/0.58  (assume t25.a0 (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))
% 0.41/0.58  (assume t25.a1 (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))
% 0.41/0.58  (assume t25.a2 (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))
% 0.41/0.58  (step t25.t1 (cl (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule implies_neg1)
% 0.41/0.58  (anchor :step t25.t2)
% 0.41/0.58  (assume t25.t2.a0 (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))
% 0.41/0.58  (assume t25.t2.a1 (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))
% 0.41/0.58  (assume t25.t2.a2 (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))
% 0.41/0.58  (step t25.t2.t1 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule equiv_simplify)
% 0.41/0.58  (step t25.t2.t2 (cl (not (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule equiv1 :premises (t25.t2.t1))
% 0.41/0.58  (step t25.t2.t3 (cl (not (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false))) (not (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false)) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false)) :rule equiv_pos2)
% 0.41/0.58  (step t25.t2.t4 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))))) :rule all_simplify)
% 0.41/0.58  (step t25.t2.t5 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule all_simplify)
% 0.41/0.58  (step t25.t2.t6 (cl (= (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule cong :premises (t25.t2.t5))
% 0.41/0.58  (step t25.t2.t7 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule trans :premises (t25.t2.t4 t25.t2.t6))
% 0.41/0.58  (step t25.t2.t8 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule all_simplify)
% 0.41/0.58  (step t25.t2.t9 (cl (= (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false))) :rule symm :premises (t25.t2.t8))
% 0.41/0.58  (step t25.t2.t10 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false) (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false))) :rule trans :premises (t25.t2.t7 t25.t2.t9))
% 0.41/0.58  (step t25.t2.t11 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c))) :rule symm :premises (t25.t2.a0))
% 0.41/0.58  (step t25.t2.t12 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) :rule symm :premises (t25.t2.a2))
% 0.41/0.58  (step t25.t2.t13 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule cong :premises (t25.t2.t11 t25.t2.t12))
% 0.41/0.58  (step t25.t2.t14 (cl (= (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) false) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) :rule equiv_simplify)
% 0.41/0.58  (step t25.t2.t15 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) false) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) :rule equiv2 :premises (t25.t2.t14))
% 0.41/0.58  (step t25.t2.t16 (cl (not (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) :rule not_not)
% 0.41/0.58  (step t25.t2.t17 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) false) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) :rule resolution :premises (t25.t2.t15 t25.t2.t16))
% 0.41/0.58  (step t25.t2.t18 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) false)) :rule resolution :premises (t25.t2.t17 t25.t2.a1))
% 0.41/0.58  (step t25.t2.t19 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) false)) :rule trans :premises (t25.t2.t13 t25.t2.t18))
% 0.41/0.58  (step t25.t2.t20 (cl (= (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) false)) :rule resolution :premises (t25.t2.t3 t25.t2.t10 t25.t2.t19))
% 0.41/0.58  (step t25.t2.t21 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t25.t2.t2 t25.t2.t20))
% 0.41/0.58  (step t25.t2 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule subproof :discharge (t25.t2.a0 t25.t2.a1 t25.t2.a2))
% 0.41/0.58  (step t25.t3 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule and_pos)
% 0.41/0.58  (step t25.t4 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule and_pos)
% 0.41/0.58  (step t25.t5 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule and_pos)
% 0.41/0.58  (step t25.t6 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))))) :rule resolution :premises (t25.t2 t25.t3 t25.t4 t25.t5))
% 0.41/0.58  (step t25.t7 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule reordering :premises (t25.t6))
% 0.41/0.58  (step t25.t8 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule contraction :premises (t25.t7))
% 0.41/0.58  (step t25.t9 (cl (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t25.t1 t25.t8))
% 0.41/0.58  (step t25.t10 (cl (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule implies_neg2)
% 0.41/0.58  (step t25.t11 (cl (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule resolution :premises (t25.t9 t25.t10))
% 0.41/0.58  (step t25.t12 (cl (=> (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule contraction :premises (t25.t11))
% 0.41/0.58  (step t25.t13 (cl (not (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule implies :premises (t25.t12))
% 0.41/0.58  (step t25.t14 (cl (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule and_neg)
% 0.41/0.58  (step t25.t15 (cl (and (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule resolution :premises (t25.t14 t25.a2 t25.a0 t25.a1))
% 0.41/0.58  (step t25.t16 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t25.t13 t25.t15))
% 0.41/0.58  (step t25 (cl (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule subproof :discharge (t25.a0 t25.a1 t25.a2))
% 0.41/0.58  (step t26 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) :rule and_pos)
% 0.41/0.58  (step t27 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule and_pos)
% 0.41/0.58  (step t28 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule and_pos)
% 0.41/0.58  (step t29 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule resolution :premises (t25 t26 t27 t28))
% 0.41/0.58  (step t30 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule reordering :premises (t29))
% 0.41/0.58  (step t31 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule contraction :premises (t30))
% 0.41/0.58  (step t32 (cl (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t24 t31))
% 0.41/0.58  (step t33 (cl (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule implies_neg2)
% 0.41/0.58  (step t34 (cl (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule resolution :premises (t32 t33))
% 0.41/0.58  (step t35 (cl (=> (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule contraction :premises (t34))
% 0.41/0.58  (step t36 (cl (not (and (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule implies :premises (t35))
% 0.41/0.58  (step t37 (cl (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t23 t36))
% 0.41/0.58  (step t38 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))))) :rule or_neg)
% 0.41/0.58  (step t39 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))))) :rule or_neg)
% 0.41/0.58  (step t40 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule or_neg)
% 0.41/0.58  (step t41 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule or_neg)
% 0.41/0.58  (step t42 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule resolution :premises (t37 t38 t39 t40 t41))
% 0.41/0.58  (step t43 (cl (or (not (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule contraction :premises (t42))
% 0.41/0.58  (step t44 (cl (or (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))))) :rule resolution :premises (t8 t22 t43))
% 0.41/0.58  (step t45 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b)) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule or :premises (t44))
% 0.41/0.58  (step t46 (cl (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A)))) :rule implies_neg1)
% 0.41/0.58  (anchor :step t47)
% 0.41/0.58  (assume t47.a0 (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))))
% 0.41/0.58  (step t47.t1 (cl (or (not (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule forall_inst :args ((:= A (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (:= B tptp.b)))
% 0.41/0.58  (step t47.t2 (cl (not (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule or :premises (t47.t1))
% 0.41/0.58  (step t47.t3 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule resolution :premises (t47.t2 t47.a0))
% 0.41/0.58  (step t47 (cl (not (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule subproof :discharge (t47.a0))
% 0.41/0.58  (step t48 (cl (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule resolution :premises (t46 t47))
% 0.41/0.58  (step t49 (cl (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule implies_neg2)
% 0.41/0.58  (step t50 (cl (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule resolution :premises (t48 t49))
% 0.41/0.58  (step t51 (cl (=> (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c))))) :rule contraction :premises (t50))
% 0.41/0.58  (step t52 (cl (not (forall ((A tptp.a) (B tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) A)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule implies :premises (t51))
% 0.41/0.58  (step t53 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)))) :rule resolution :premises (t52 a1))
% 0.41/0.58  (step t54 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C))))) :rule implies_neg1)
% 0.41/0.58  (anchor :step t55)
% 0.41/0.58  (assume t55.a0 (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))))
% 0.41/0.58  (step t55.t1 (cl (or (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule forall_inst :args ((:= A tptp.a2) (:= B tptp.b) (:= C tptp.c)))
% 0.41/0.58  (step t55.t2 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule or :premises (t55.t1))
% 0.41/0.58  (step t55.t3 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule resolution :premises (t55.t2 t55.a0))
% 0.41/0.58  (step t55 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule subproof :discharge (t55.a0))
% 0.41/0.59  (step t56 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule resolution :premises (t54 t55))
% 0.41/0.59  (step t57 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule implies_neg2)
% 0.41/0.59  (step t58 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t56 t57))
% 0.41/0.59  (step t59 (cl (=> (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C)))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule contraction :premises (t58))
% 0.41/0.59  (step t60 (cl (not (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) B)) C) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f A) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f B) C))))) (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule implies :premises (t59))
% 0.41/0.59  (step t61 (cl (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.b)) tptp.c) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c)))) :rule resolution :premises (t60 a3))
% 0.41/0.59  (step t62 (cl (not (= (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) tptp.c)) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.a2) (tptp.aa_a_a (tptp.aa_a_fun_a_a tptp.f tptp.b) tptp.c))))) :rule resolution :premises (t45 a12 t53 t61))
% 0.41/0.59  (step t63 (cl) :rule resolution :premises (t7 t62 a2))
% 0.41/0.59  
% 0.41/0.59  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.WXGljJ12Jm/cvc5---1.0.5_31519.smt2
% 0.41/0.59  % cvc5---1.0.5 exiting
% 0.41/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------