TSTP Solution File: NUM415^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n017.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 17:33:15 EDT 2024
% Result : Theorem 0.23s 0.55s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% 0.14/0.16 % Command : do_cvc5 %s %d
% 0.16/0.38 % Computer : n017.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Tue May 28 02:51:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.23/0.52 %----Proving TH0
% 0.23/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.55 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.dK9hvkYG8k/cvc5---1.0.5_25714.smt2
% 0.23/0.55 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.dK9hvkYG8k/cvc5---1.0.5_25714.smt2
% 0.23/0.55 (assume a0 (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y)))
% 0.23/0.55 (assume a1 (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))
% 0.23/0.55 (assume a2 (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))))
% 0.23/0.55 (assume a3 (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))))
% 0.23/0.55 (assume a4 (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y)))))))
% 0.23/0.55 (assume a5 (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))))
% 0.23/0.55 (assume a6 (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))
% 0.23/0.55 (assume a7 (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))
% 0.23/0.55 (assume a8 (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))
% 0.23/0.55 (assume a9 (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))
% 0.23/0.55 (assume a10 (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))
% 0.23/0.55 (assume a11 (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y)))))
% 0.23/0.55 (assume a12 (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y)))))
% 0.23/0.55 (assume a13 (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y))))
% 0.23/0.55 (assume a14 (not (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one)))))
% 0.23/0.55 (assume a15 true)
% 0.23/0.55 (step t1 (cl (not (= (not (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one)))) false)) (not (not (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one))))) false) :rule equiv_pos2)
% 0.23/0.55 (step t2 (cl (and (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y))) (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y)))) (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y)))) (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y)))))) (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y))) (not (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)))) (not (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))))) (not (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))))) (not (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) (not (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (not (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (not (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (not (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (not (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (not (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y))))))) (not (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))))) (not (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))))) (not (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))) (not (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y)))) :rule and_neg)
% 0.23/0.55 (step t3 (cl (and (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y))) (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y)))) (= tptp.succ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y)))) (= tptp.ten (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (= tptp.nine (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (= tptp.eight (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (= tptp.six (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (= tptp.four (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X Y)))))) (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (= tptp.zero (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) Y)))) :rule resolution :premises (t2 a13 a12 a11 a10 a9 a8 a7 a6 a5 a4 a3 a2 a1 a0))
% 0.23/0.55 (step t4 (cl (= tptp.mult (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)))) :rule and :premises (t3))
% 0.23/0.55 (step t5 (cl (= tptp.two (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))))) :rule and :premises (t3))
% 0.23/0.55 (step t6 (cl (= (@ tptp.mult tptp.two) (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))))) :rule cong :premises (t4 t5))
% 0.23/0.55 (step t7 (cl (= tptp.plus (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))))) :rule and :premises (t3))
% 0.23/0.55 (step t8 (cl (= tptp.three (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))))) :rule and :premises (t3))
% 0.23/0.55 (step t9 (cl (= (@ tptp.plus tptp.three) (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))))) :rule cong :premises (t7 t8))
% 0.23/0.55 (step t10 (cl (= tptp.seven (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule and :premises (t3))
% 0.23/0.55 (step t11 (cl (= (@ (@ tptp.plus tptp.three) tptp.seven) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) :rule cong :premises (t9 t10))
% 0.23/0.55 (step t12 (cl (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule cong :premises (t6 t11))
% 0.23/0.55 (step t13 (cl (= tptp.five (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule and :premises (t3))
% 0.23/0.55 (step t14 (cl (= (@ (@ tptp.mult tptp.two) tptp.five) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))))) :rule cong :premises (t6 t13))
% 0.23/0.55 (step t15 (cl (= (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule cong :premises (t4 t14))
% 0.23/0.55 (step t16 (cl (= tptp.one (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))) :rule and :premises (t3))
% 0.23/0.55 (step t17 (cl (= (@ tptp.plus tptp.one) (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) :rule cong :premises (t7 t16))
% 0.23/0.55 (step t18 (cl (= (@ (@ tptp.plus tptp.one) tptp.one) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) :rule cong :premises (t17 t16))
% 0.23/0.55 (step t19 (cl (= (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))))) :rule cong :premises (t15 t18))
% 0.23/0.55 (step t20 (cl (= (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one))) (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))))) :rule cong :premises (t12 t19))
% 0.23/0.55 (step t21 (cl (= (not (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one)))) (not (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))))))) :rule cong :premises (t20))
% 0.23/0.55 (step t22 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) (@ N X)) Y)))) :rule all_simplify)
% 0.23/0.55 (anchor :step t23 :args ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (:= N N) (X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t23.t1 (cl (= N N)) :rule refl)
% 0.23/0.55 (step t23.t2 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t23.t3 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t23.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) (@ N X)) (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))))) :rule all_simplify)
% 0.23/0.55 (step t23.t5 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t23.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) (@ N X)) Y) (@ (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) Y))) :rule cong :premises (t23.t4 t23.t5))
% 0.23/0.55 (step t23.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) Y) (@ (@ N X) (@ (@ N X) Y)))) :rule all_simplify)
% 0.23/0.55 (step t23.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) (@ N X)) Y) (@ (@ N X) (@ (@ N X) Y)))) :rule trans :premises (t23.t6 t23.t7))
% 0.23/0.55 (step t23 (cl (= (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) (@ N X)) Y)) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))))) :rule bind)
% 0.23/0.55 (step t24 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))))) :rule trans :premises (t22 t23))
% 0.23/0.55 (step t25 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))) X) (@ (@ N X) Y))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t26 :args ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (:= N N) (X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t26.t1 (cl (= N N)) :rule refl)
% 0.23/0.55 (step t26.t2 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t26.t3 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t26.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))) X) (lambda ((Y $$unsorted)) (@ X (@ X (@ X Y)))))) :rule all_simplify)
% 0.23/0.55 (step t26.t5 (cl (= (@ (@ N X) Y) (@ (@ N X) Y))) :rule refl)
% 0.23/0.55 (step t26.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))) X) (@ (@ N X) Y)) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X Y)))) (@ (@ N X) Y)))) :rule cong :premises (t26.t4 t26.t5))
% 0.23/0.55 (step t26.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X Y)))) (@ (@ N X) Y)) (@ X (@ X (@ X (@ (@ N X) Y)))))) :rule all_simplify)
% 0.23/0.55 (step t26.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))) X) (@ (@ N X) Y)) (@ X (@ X (@ X (@ (@ N X) Y)))))) :rule trans :premises (t26.t6 t26.t7))
% 0.23/0.55 (step t26 (cl (= (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y)))) X) (@ (@ N X) Y))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ N X) Y))))))) :rule bind)
% 0.23/0.55 (step t27 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ N X) Y))))))) :rule trans :premises (t25 t26))
% 0.23/0.55 (step t28 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule refl)
% 0.23/0.55 (step t29 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ N X) Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) :rule cong :premises (t27 t28))
% 0.23/0.55 (step t30 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ N X) Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y))))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t31 :args ((X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t31.t1 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t31.t2 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t31.t3 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t31.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule all_simplify)
% 0.23/0.55 (step t31.t5 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t31.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) Y))) :rule cong :premises (t31.t4 t31.t5))
% 0.23/0.55 (step t31.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) Y) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) :rule all_simplify)
% 0.23/0.55 (step t31.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) :rule trans :premises (t31.t6 t31.t7))
% 0.23/0.55 (step t31.t9 (cl (= (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule cong :premises (t31.t3 t31.t8))
% 0.23/0.55 (step t31.t10 (cl (= (@ X (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) :rule cong :premises (t31.t3 t31.t9))
% 0.23/0.55 (step t31.t11 (cl (= (@ X (@ X (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y)))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule cong :premises (t31.t3 t31.t10))
% 0.23/0.55 (step t31 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) X) Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule bind)
% 0.23/0.55 (step t32 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ (@ N X) Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule trans :premises (t30 t31))
% 0.23/0.55 (step t33 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule trans :premises (t29 t32))
% 0.23/0.55 (step t34 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))) :rule cong :premises (t24 t33))
% 0.23/0.55 (step t35 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t36 :args ((X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t36.t1 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t36.t2 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t36.t3 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t36.t4 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t36.t5 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) Y))) :rule cong :premises (t36.t3 t36.t4))
% 0.23/0.55 (step t36.t6 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) Y) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule all_simplify)
% 0.23/0.55 (step t36.t7 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule trans :premises (t36.t5 t36.t6))
% 0.23/0.55 (step t36.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y)) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule cong :premises (t36.t3 t36.t7))
% 0.23/0.55 (step t36.t9 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t36.t10 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))) :rule trans :premises (t36.t8 t36.t9))
% 0.23/0.55 (step t36 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule bind)
% 0.23/0.55 (step t37 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule trans :premises (t35 t36))
% 0.23/0.55 (step t38 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule trans :premises (t34 t37))
% 0.23/0.55 (step t39 (cl (= (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)))) :rule refl)
% 0.23/0.55 (step t40 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule refl)
% 0.23/0.55 (step t41 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))))) :rule cong :premises (t24 t40))
% 0.23/0.55 (step t42 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t43 :args ((X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t43.t1 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t43.t2 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t43.t3 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule all_simplify)
% 0.23/0.55 (step t43.t4 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t43.t5 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) Y))) :rule cong :premises (t43.t3 t43.t4))
% 0.23/0.55 (step t43.t6 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) Y) (@ X (@ X (@ X (@ X (@ X Y))))))) :rule all_simplify)
% 0.23/0.55 (step t43.t7 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y) (@ X (@ X (@ X (@ X (@ X Y))))))) :rule trans :premises (t43.t5 t43.t6))
% 0.23/0.55 (step t43.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y)) (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule cong :premises (t43.t3 t43.t7))
% 0.23/0.55 (step t43.t9 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) (@ X (@ X (@ X (@ X (@ X Y)))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule all_simplify)
% 0.23/0.55 (step t43.t10 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule trans :premises (t43.t8 t43.t9))
% 0.23/0.55 (step t43 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))) X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule bind)
% 0.23/0.55 (step t44 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule trans :premises (t42 t43))
% 0.23/0.55 (step t45 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule trans :premises (t41 t44))
% 0.23/0.55 (step t46 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))) :rule cong :premises (t39 t45))
% 0.23/0.55 (step t47 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ N X)) Y)))) :rule all_simplify)
% 0.23/0.55 (anchor :step t48 :args ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (:= N N) (X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t48.t1 (cl (= N N)) :rule refl)
% 0.23/0.55 (step t48.t2 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t48.t3 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t48.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ N X)) (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t48.t5 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t48.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ N X)) Y) (@ (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))) Y))) :rule cong :premises (t48.t4 t48.t5))
% 0.23/0.55 (step t48.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))) Y) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y)))))))))))) :rule all_simplify)
% 0.23/0.55 (step t48.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ N X)) Y) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y)))))))))))) :rule trans :premises (t48.t6 t48.t7))
% 0.23/0.55 (step t48 (cl (= (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ N X)) Y)) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))))) :rule bind)
% 0.23/0.55 (step t49 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))))) :rule trans :premises (t47 t48))
% 0.23/0.55 (step t50 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))))) :rule trans :premises (t46 t49))
% 0.23/0.55 (step t51 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (@ (@ N X) Y))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t52 :args ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (:= N N) (X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t52.t1 (cl (= N N)) :rule refl)
% 0.23/0.55 (step t52.t2 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t52.t3 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t52.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (lambda ((Y $$unsorted)) (@ X Y)))) :rule all_simplify)
% 0.23/0.55 (step t52.t5 (cl (= (@ (@ N X) Y) (@ (@ N X) Y))) :rule refl)
% 0.23/0.55 (step t52.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (@ (@ N X) Y)) (@ (lambda ((Y $$unsorted)) (@ X Y)) (@ (@ N X) Y)))) :rule cong :premises (t52.t4 t52.t5))
% 0.23/0.55 (step t52.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ X Y)) (@ (@ N X) Y)) (@ X (@ (@ N X) Y)))) :rule all_simplify)
% 0.23/0.55 (step t52.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (@ (@ N X) Y)) (@ X (@ (@ N X) Y)))) :rule trans :premises (t52.t6 t52.t7))
% 0.23/0.55 (step t52 (cl (= (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (@ (@ N X) Y))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))))) :rule bind)
% 0.23/0.55 (step t53 (cl (= (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))))) :rule trans :premises (t51 t52))
% 0.23/0.55 (step t54 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))) :rule refl)
% 0.23/0.55 (step t55 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) :rule cong :premises (t53 t54))
% 0.23/0.55 (step t56 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) Y))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t57 :args ((X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t57.t1 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t57.t2 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t57.t3 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t57.t4 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) (lambda ((Y $$unsorted)) (@ X Y)))) :rule all_simplify)
% 0.23/0.55 (step t57.t5 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t57.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) Y) (@ (lambda ((Y $$unsorted)) (@ X Y)) Y))) :rule cong :premises (t57.t4 t57.t5))
% 0.23/0.55 (step t57.t7 (cl (= (@ (lambda ((Y $$unsorted)) (@ X Y)) Y) (@ X Y))) :rule all_simplify)
% 0.23/0.55 (step t57.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) Y) (@ X Y))) :rule trans :premises (t57.t6 t57.t7))
% 0.23/0.55 (step t57.t9 (cl (= (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) Y)) (@ X (@ X Y)))) :rule cong :premises (t57.t3 t57.t8))
% 0.23/0.55 (step t57 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)) X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))))) :rule bind)
% 0.23/0.55 (step t58 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))))) :rule trans :premises (t56 t57))
% 0.23/0.55 (step t59 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))))) :rule trans :premises (t55 t58))
% 0.23/0.55 (step t60 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))) (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))))) :rule cong :premises (t50 t59))
% 0.23/0.55 (step t61 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))))))))) :rule all_simplify)
% 0.23/0.55 (anchor :step t62 :args ((X (-> $$unsorted $$unsorted)) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.23/0.55 (step t62.t1 (cl (= X X)) :rule refl)
% 0.23/0.55 (step t62.t2 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t62.t3 (cl (= (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (lambda ((Y $$unsorted)) (@ X (@ X Y))))) :rule all_simplify)
% 0.23/0.55 (step t62.t4 (cl (= Y Y)) :rule refl)
% 0.23/0.55 (step t62.t5 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) Y))) :rule cong :premises (t62.t3 t62.t4))
% 0.23/0.55 (step t62.t6 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) Y) (@ X (@ X Y)))) :rule all_simplify)
% 0.23/0.55 (step t62.t7 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y) (@ X (@ X Y)))) :rule trans :premises (t62.t5 t62.t6))
% 0.23/0.55 (step t62.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X Y))))) :rule cong :premises (t62.t3 t62.t7))
% 0.23/0.55 (step t62.t9 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X Y))) (@ X (@ X (@ X (@ X Y)))))) :rule all_simplify)
% 0.23/0.55 (step t62.t10 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)) (@ X (@ X (@ X (@ X Y)))))) :rule trans :premises (t62.t8 t62.t9))
% 0.23/0.55 (step t62.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X Y))))))) :rule cong :premises (t62.t3 t62.t10))
% 0.23/0.55 (step t62.t12 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X Y))))) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))) (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))) :rule trans :premises (t62.t11 t62.t12))
% 0.23/0.55 (step t62.t14 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) :rule cong :premises (t62.t3 t62.t13))
% 0.23/0.55 (step t62.t15 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X Y))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) :rule trans :premises (t62.t14 t62.t15))
% 0.23/0.55 (step t62.t17 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) :rule cong :premises (t62.t3 t62.t16))
% 0.23/0.55 (step t62.t18 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t19 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))) :rule trans :premises (t62.t17 t62.t18))
% 0.23/0.55 (step t62.t20 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) :rule cong :premises (t62.t3 t62.t19))
% 0.23/0.55 (step t62.t21 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t22 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))) :rule trans :premises (t62.t20 t62.t21))
% 0.23/0.55 (step t62.t23 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))) :rule cong :premises (t62.t3 t62.t22))
% 0.23/0.55 (step t62.t24 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t25 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))) :rule trans :premises (t62.t23 t62.t24))
% 0.23/0.55 (step t62.t26 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))) :rule cong :premises (t62.t3 t62.t25))
% 0.23/0.55 (step t62.t27 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t28 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))) :rule trans :premises (t62.t26 t62.t27))
% 0.23/0.55 (step t62.t29 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))) :rule cong :premises (t62.t3 t62.t28))
% 0.23/0.55 (step t62.t30 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t31 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))) :rule trans :premises (t62.t29 t62.t30))
% 0.23/0.55 (step t62.t32 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))))))) (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))) :rule cong :premises (t62.t3 t62.t31))
% 0.23/0.55 (step t62.t33 (cl (= (@ (lambda ((Y $$unsorted)) (@ X (@ X Y))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))) :rule all_simplify)
% 0.23/0.55 (step t62.t34 (cl (= (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y)))))))))) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))) :rule trans :premises (t62.t32 t62.t33))
% 0.23/0.55 (step t62 (cl (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) (@ (@ (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y))) X) Y))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule bind)
% 0.23/0.55 (step t63 (cl (= (@ (lambda ((N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) (@ (@ N X) Y))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule trans :premises (t61 t62))
% 0.23/0.55 (step t64 (cl (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))))) :rule trans :premises (t60 t63))
% 0.23/0.55 (step t65 (cl (= (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))))) :rule cong :premises (t38 t64))
% 0.23/0.55 (step t66 (cl (= (= (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y))))))))))))))))))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))))))))))))))) true)) :rule all_simplify)
% 0.23/0.55 (step t67 (cl (= (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))))) true)) :rule trans :premises (t65 t66))
% 0.23/0.55 (step t68 (cl (= (not (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))))) (not true))) :rule cong :premises (t67))
% 0.23/0.55 (step t69 (cl (= (not true) false)) :rule all_simplify)
% 0.23/0.55 (step t70 (cl (= (not (= (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X Y))))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X (@ X (@ X Y)))))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M (@ N X)) Y)) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X Y)))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X (@ X (@ X (@ X (@ X Y)))))))) (@ (@ (lambda ((M (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (N (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)) (X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ (@ M X) (@ (@ N X) Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y))) (lambda ((X (-> $$unsorted $$unsorted)) (Y $$unsorted)) (@ X Y)))))) false)) :rule trans :premises (t68 t69))
% 0.23/0.55 (step t71 (cl (= (not (= (@ (@ tptp.mult tptp.two) (@ (@ tptp.plus tptp.three) tptp.seven)) (@ (@ tptp.mult (@ (@ tptp.mult tptp.two) tptp.five)) (@ (@ tptp.plus tptp.one) tptp.one)))) false)) :rule trans :premises (t21 t70))
% 0.23/0.55 (step t72 (cl false) :rule resolution :premises (t1 t71 a14))
% 0.23/0.55 (step t73 (cl (not false)) :rule false)
% 0.23/0.55 (step t74 (cl) :rule resolution :premises (t72 t73))
% 0.23/0.55
% 0.23/0.55 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.dK9hvkYG8k/cvc5---1.0.5_25714.smt2
% 0.23/0.55 % cvc5---1.0.5 exiting
% 0.23/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------