%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW650_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 18:20:20 EDT 2024

% Result   : Theorem 0.50s 0.73s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWW650_2 : TPTP v8.2.0. Released v6.1.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 26 04:42:39 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_ARI
% 0.50/0.73  --- Run --finite-model-find --decision=internal at 15...
% 0.50/0.73  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.50/0.73  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.DMvtOlqnq7/cvc5---1.0.5_30082.smt2
% 0.50/0.73  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.DMvtOlqnq7/cvc5---1.0.5_30082.smt2
% 0.50/0.73  (assume a0 (forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))))
% 0.50/0.73  (assume a1 (forall ((A tptp.ty) (X tptp.bool1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_bool1 A X X1 X2))))
% 0.50/0.73  (assume a2 (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_bool1 A tptp.true1 Z Z1) Z))))
% 0.50/0.73  (assume a3 (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_bool1 A tptp.false1 Z Z1) Z1))))
% 0.50/0.73  (assume a4 (not (= tptp.true1 tptp.false1)))
% 0.50/0.73  (assume a5 (forall ((U tptp.bool1)) (or (= U tptp.true1) (= U tptp.false1))))
% 0.50/0.73  (assume a6 (forall ((U tptp.tuple02)) (= U tptp.tuple03)))
% 0.50/0.73  (assume a7 (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))))
% 0.50/0.73  (assume a8 (forall ((X tptp.t1)) (= (tptp.iter1 0 X) X)))
% 0.50/0.73  (assume a9 (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X))))))
% 0.50/0.73  (assume a10 (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))))
% 0.50/0.73  (assume a11 (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.f1 (tptp.iter1 (- K 1) X))))))
% 0.50/0.73  (assume a12 (<= 0 tptp.mu1))
% 0.50/0.73  (assume a13 (<= 1 tptp.lambda1))
% 0.50/0.73  (assume a14 (forall ((I Int) (J Int)) (=> (and (<= 0 I) (< I (+ tptp.mu1 tptp.lambda1))) (=> (and (<= 0 J) (< J (+ tptp.mu1 tptp.lambda1))) (=> (not (= I J)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 J tptp.x01))))))))
% 0.50/0.73  (assume a15 (forall ((N Int)) (=> (<= tptp.mu1 N) (= (tptp.iter1 (+ N tptp.lambda1) tptp.x01) (tptp.iter1 N tptp.x01)))))
% 0.50/0.73  (assume a16 (forall ((N Int)) (=> (<= tptp.mu1 N) (forall ((K Int)) (=> (<= 0 K) (= (tptp.iter1 (+ N (* tptp.lambda1 K)) tptp.x01) (tptp.iter1 N tptp.x01)))))))
% 0.50/0.73  (assume a17 (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.ref A) (tptp.mk_ref A X))))
% 0.50/0.73  (assume a18 (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.contents A X))))
% 0.50/0.73  (assume a19 (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.contents A (tptp.mk_ref A U)) U))))
% 0.50/0.73  (assume a20 (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))))
% 0.50/0.73  (assume a21 (forall ((I Int) (J Int)) (=> (<= tptp.mu1 I) (=> (<= tptp.mu1 J) (and (<= 0 (tptp.dist1 I J)) (= (tptp.iter1 (+ I (tptp.dist1 I J)) tptp.x01) (tptp.iter1 J tptp.x01)) (forall ((K Int)) (=> (<= 0 K) (=> (= (tptp.iter1 (+ I K) tptp.x01) (tptp.iter1 J tptp.x01)) (<= (tptp.dist1 I J) K)))))))))
% 0.50/0.73  (assume a22 (forall ((T2 tptp.t1) (T1 tptp.t1)) (= (tptp.rel1 T2 T1) (exists ((I Int)) (and (= T1 (tptp.iter1 I tptp.x01)) (= T2 (tptp.iter1 (+ I 1) tptp.x01)) (<= 1 I) (<= I (+ tptp.mu1 tptp.lambda1)) (=> (<= tptp.mu1 I) (< (tptp.dist1 (+ (* 2 I) 2) (+ I 1)) (tptp.dist1 (* 2 I) I))))))))
% 0.50/0.73  (assume a23 (not (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))
% 0.50/0.73  (assume a24 true)
% 0.50/0.73  (step t1 (cl (not (= (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule equiv_pos2)
% 0.50/0.73  (step t2 (cl (= (not (>= tptp.mu1 0)) (not (>= tptp.mu1 0)))) :rule refl)
% 0.50/0.73  (step t3 (cl (= (not (>= tptp.lambda1 1)) (not (>= tptp.lambda1 1)))) :rule refl)
% 0.50/0.73  (step t4 (cl (= (= (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1)) true) (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule equiv_simplify)
% 0.50/0.73  (step t5 (cl (not (= (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1)) true)) (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule equiv1 :premises (t4))
% 0.50/0.73  (step t6 (cl (= (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1)) (= (>= (+ tptp.mu1 tptp.lambda1) 1) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))))) :rule all_simplify)
% 0.50/0.73  (step t7 (cl (= (>= (+ tptp.mu1 tptp.lambda1) 1) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule refl)
% 0.50/0.73  (step t8 (cl (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule all_simplify)
% 0.50/0.73  (step t9 (cl (= (= (>= (+ tptp.mu1 tptp.lambda1) 1) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (= (>= (+ tptp.mu1 tptp.lambda1) 1) (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule cong :premises (t7 t8))
% 0.50/0.73  (step t10 (cl (= (= (>= (+ tptp.mu1 tptp.lambda1) 1) (>= (+ tptp.mu1 tptp.lambda1) 1)) true)) :rule all_simplify)
% 0.50/0.73  (step t11 (cl (= (= (>= (+ tptp.mu1 tptp.lambda1) 1) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) true)) :rule trans :premises (t9 t10))
% 0.50/0.73  (step t12 (cl (= (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1)) true)) :rule trans :premises (t6 t11))
% 0.50/0.73  (step t13 (cl (= (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule resolution :premises (t5 t12))
% 0.50/0.73  (step t14 (cl (= (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule cong :premises (t2 t3 t13))
% 0.50/0.73  (step t15 (cl (not (= (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))))) (not (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule equiv_pos2)
% 0.50/0.73  (step t16 (cl (= (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule refl)
% 0.50/0.73  (step t17 (cl (= (= (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))))) :rule equiv_simplify)
% 0.50/0.73  (step t18 (cl (= (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (not (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))))) :rule equiv2 :premises (t17))
% 0.50/0.73  (step t19 (cl (not (not (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule not_not)
% 0.50/0.73  (step t20 (cl (= (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule resolution :premises (t18 t19))
% 0.50/0.73  (step t21 (cl (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t22)
% 0.50/0.73  (assume t22.a0 (>= tptp.lambda1 1))
% 0.50/0.73  (assume t22.a1 (not (>= (+ tptp.mu1 tptp.lambda1) 1)))
% 0.50/0.73  (assume t22.a2 (>= tptp.mu1 0))
% 0.50/0.73  (step t22.t1 (cl (not (= (< tptp.mu1 0) (not (>= tptp.mu1 0)))) (not (< tptp.mu1 0)) (not (>= tptp.mu1 0))) :rule equiv_pos2)
% 0.50/0.73  (step t22.t2 (cl (= (< tptp.mu1 0) (not (>= tptp.mu1 0)))) :rule all_simplify)
% 0.50/0.73  (step t22.t3 (cl (not (= (not (>= tptp.mu1 0)) (< tptp.mu1 0))) (not (not (>= tptp.mu1 0))) (< tptp.mu1 0)) :rule equiv_pos2)
% 0.50/0.73  (step t22.t4 (cl (= (not (>= tptp.mu1 0)) (< tptp.mu1 0))) :rule symm :premises (t22.t2))
% 0.50/0.73  (step t22.t5 (cl (=> (>= tptp.mu1 0) false) (>= tptp.mu1 0)) :rule implies_neg1)
% 0.50/0.73  (anchor :step t22.t6)
% 0.50/0.73  (assume t22.t6.a0 (>= tptp.mu1 0))
% 0.50/0.73  (step t22.t6.t1 (cl (not (= (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1))) false)) (not (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))) false) :rule equiv_pos2)
% 0.50/0.73  (step t22.t6.t2 (cl (= (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1))) (not (>= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t3 (cl (= (* (- 1.0) tptp.mu1) (to_real (* (- 1) tptp.mu1)))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t4 (cl (= (* 1.0 (+ tptp.mu1 tptp.lambda1)) (to_real (+ tptp.mu1 tptp.lambda1)))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t5 (cl (= (* (- 1.0) tptp.lambda1) (to_real (* (- 1) tptp.lambda1)))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t6 (cl (= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (to_real (* (- 1) tptp.mu1)) (to_real (+ tptp.mu1 tptp.lambda1)) (to_real (* (- 1) tptp.lambda1))))) :rule cong :premises (t22.t6.t3 t22.t6.t4 t22.t6.t5))
% 0.50/0.73  (step t22.t6.t7 (cl (= (+ (to_real (* (- 1) tptp.mu1)) (to_real (+ tptp.mu1 tptp.lambda1)) (to_real (* (- 1) tptp.lambda1))) 0.0)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t8 (cl (= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) 0.0)) :rule trans :premises (t22.t6.t6 t22.t6.t7))
% 0.50/0.73  (step t22.t6.t9 (cl (= (* (- 1.0) 0) 0.0)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t10 (cl (= (* 1.0 1) 1.0)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t11 (cl (= (* (- 1.0) 1) (- 1.0))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t12 (cl (= (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)) (+ 0.0 1.0 (- 1.0)))) :rule cong :premises (t22.t6.t9 t22.t6.t10 t22.t6.t11))
% 0.50/0.73  (step t22.t6.t13 (cl (= (+ 0.0 1.0 (- 1.0)) 0.0)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t14 (cl (= (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)) 0.0)) :rule trans :premises (t22.t6.t12 t22.t6.t13))
% 0.50/0.73  (step t22.t6.t15 (cl (= (>= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1))) (>= 0.0 0.0))) :rule cong :premises (t22.t6.t8 t22.t6.t14))
% 0.50/0.73  (step t22.t6.t16 (cl (= (>= 0.0 0.0) true)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t17 (cl (= (>= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1))) true)) :rule trans :premises (t22.t6.t15 t22.t6.t16))
% 0.50/0.73  (step t22.t6.t18 (cl (= (not (>= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))) (not true))) :rule cong :premises (t22.t6.t17))
% 0.50/0.73  (step t22.t6.t19 (cl (= (not true) false)) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t20 (cl (= (not (>= (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))) false)) :rule trans :premises (t22.t6.t18 t22.t6.t19))
% 0.50/0.73  (step t22.t6.t21 (cl (= (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1))) false)) :rule trans :premises (t22.t6.t2 t22.t6.t20))
% 0.50/0.73  (step t22.t6.t22 (cl (not (<= (* (- 1.0) tptp.mu1) (* (- 1.0) 0))) (not (< (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* 1.0 1))) (not (<= (* (- 1.0) tptp.lambda1) (* (- 1.0) 1))) (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))) :rule la_generic :args (1 1 1 1))
% 0.50/0.73  (step t22.t6.t23 (cl (=> (and (< (- 1.0) 0) (>= tptp.mu1 0)) (<= (* (- 1.0) tptp.mu1) (* (- 1.0) 0)))) :rule la_mult_neg)
% 0.50/0.73  (step t22.t6.t24 (cl (not (and (< (- 1.0) 0) (>= tptp.mu1 0))) (<= (* (- 1.0) tptp.mu1) (* (- 1.0) 0))) :rule implies :premises (t22.t6.t23))
% 0.50/0.73  (step t22.t6.t25 (cl (and (< (- 1.0) 0) (>= tptp.mu1 0)) (not (< (- 1.0) 0)) (not (>= tptp.mu1 0))) :rule and_neg)
% 0.50/0.73  (step t22.t6.t26 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.50/0.73  (step t22.t6.t27 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t22.t6.t26))
% 0.50/0.73  (step t22.t6.t28 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.50/0.73  (step t22.t6.t29 (cl (< (- 1.0) 0)) :rule resolution :premises (t22.t6.t27 t22.t6.t28))
% 0.50/0.73  (step t22.t6.t30 (cl (and (< (- 1.0) 0) (>= tptp.mu1 0))) :rule resolution :premises (t22.t6.t25 t22.t6.t29 t22.t6.a0))
% 0.50/0.73  (step t22.t6.t31 (cl (<= (* (- 1.0) tptp.mu1) (* (- 1.0) 0))) :rule resolution :premises (t22.t6.t24 t22.t6.t30))
% 0.50/0.73  (step t22.t6.t32 (cl (=> (and (> 1.0 0) (< (+ tptp.mu1 tptp.lambda1) 1)) (< (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* 1.0 1)))) :rule la_mult_pos)
% 0.50/0.73  (step t22.t6.t33 (cl (not (and (> 1.0 0) (< (+ tptp.mu1 tptp.lambda1) 1))) (< (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* 1.0 1))) :rule implies :premises (t22.t6.t32))
% 0.50/0.73  (step t22.t6.t34 (cl (and (> 1.0 0) (< (+ tptp.mu1 tptp.lambda1) 1)) (not (> 1.0 0)) (not (< (+ tptp.mu1 tptp.lambda1) 1))) :rule and_neg)
% 0.50/0.73  (step t22.t6.t35 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.50/0.73  (step t22.t6.t36 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t22.t6.t35))
% 0.50/0.73  (step t22.t6.t37 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.50/0.73  (step t22.t6.t38 (cl (> 1.0 0)) :rule resolution :premises (t22.t6.t36 t22.t6.t37))
% 0.50/0.73  (step t22.t6.t39 (cl (not (= (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (< (+ tptp.mu1 tptp.lambda1) 1))) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (< (+ tptp.mu1 tptp.lambda1) 1)) :rule equiv_pos2)
% 0.50/0.73  (step t22.t6.t40 (cl (= (< (+ tptp.mu1 tptp.lambda1) 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule all_simplify)
% 0.50/0.73  (step t22.t6.t41 (cl (= (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (< (+ tptp.mu1 tptp.lambda1) 1))) :rule symm :premises (t22.t6.t40))
% 0.50/0.73  (step t22.t6.t42 (cl (< (+ tptp.mu1 tptp.lambda1) 1)) :rule resolution :premises (t22.t6.t39 t22.t6.t41 t22.a1))
% 0.50/0.73  (step t22.t6.t43 (cl (and (> 1.0 0) (< (+ tptp.mu1 tptp.lambda1) 1))) :rule resolution :premises (t22.t6.t34 t22.t6.t38 t22.t6.t42))
% 0.50/0.73  (step t22.t6.t44 (cl (< (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* 1.0 1))) :rule resolution :premises (t22.t6.t33 t22.t6.t43))
% 0.50/0.73  (step t22.t6.t45 (cl (=> (and (< (- 1.0) 0) (>= tptp.lambda1 1)) (<= (* (- 1.0) tptp.lambda1) (* (- 1.0) 1)))) :rule la_mult_neg)
% 0.50/0.73  (step t22.t6.t46 (cl (not (and (< (- 1.0) 0) (>= tptp.lambda1 1))) (<= (* (- 1.0) tptp.lambda1) (* (- 1.0) 1))) :rule implies :premises (t22.t6.t45))
% 0.50/0.73  (step t22.t6.t47 (cl (and (< (- 1.0) 0) (>= tptp.lambda1 1)) (not (< (- 1.0) 0)) (not (>= tptp.lambda1 1))) :rule and_neg)
% 0.50/0.73  (step t22.t6.t48 (cl (and (< (- 1.0) 0) (>= tptp.lambda1 1))) :rule resolution :premises (t22.t6.t47 t22.t6.t29 t22.a0))
% 0.50/0.73  (step t22.t6.t49 (cl (<= (* (- 1.0) tptp.lambda1) (* (- 1.0) 1))) :rule resolution :premises (t22.t6.t46 t22.t6.t48))
% 0.50/0.73  (step t22.t6.t50 (cl (< (+ (* (- 1.0) tptp.mu1) (* 1.0 (+ tptp.mu1 tptp.lambda1)) (* (- 1.0) tptp.lambda1)) (+ (* (- 1.0) 0) (* 1.0 1) (* (- 1.0) 1)))) :rule resolution :premises (t22.t6.t22 t22.t6.t31 t22.t6.t44 t22.t6.t49))
% 0.50/0.73  (step t22.t6.t51 (cl false) :rule resolution :premises (t22.t6.t1 t22.t6.t21 t22.t6.t50))
% 0.50/0.73  (step t22.t6 (cl (not (>= tptp.mu1 0)) false) :rule subproof :discharge (t22.t6.a0))
% 0.50/0.73  (step t22.t7 (cl (=> (>= tptp.mu1 0) false) false) :rule resolution :premises (t22.t5 t22.t6))
% 0.50/0.73  (step t22.t8 (cl (=> (>= tptp.mu1 0) false) (not false)) :rule implies_neg2)
% 0.50/0.73  (step t22.t9 (cl (=> (>= tptp.mu1 0) false) (=> (>= tptp.mu1 0) false)) :rule resolution :premises (t22.t7 t22.t8))
% 0.50/0.73  (step t22.t10 (cl (=> (>= tptp.mu1 0) false)) :rule contraction :premises (t22.t9))
% 0.50/0.73  (step t22.t11 (cl (= (=> (>= tptp.mu1 0) false) (not (>= tptp.mu1 0)))) :rule implies_simplify)
% 0.50/0.73  (step t22.t12 (cl (not (=> (>= tptp.mu1 0) false)) (not (>= tptp.mu1 0))) :rule equiv1 :premises (t22.t11))
% 0.50/0.73  (step t22.t13 (cl (not (>= tptp.mu1 0))) :rule resolution :premises (t22.t10 t22.t12))
% 0.50/0.73  (step t22.t14 (cl (< tptp.mu1 0)) :rule resolution :premises (t22.t3 t22.t4 t22.t13))
% 0.50/0.73  (step t22.t15 (cl (not (>= tptp.mu1 0))) :rule resolution :premises (t22.t1 t22.t2 t22.t14))
% 0.50/0.73  (step t22.t16 (cl) :rule resolution :premises (t22.a2 t22.t15))
% 0.50/0.73  (step t22 (cl (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (not (>= tptp.mu1 0)) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.50/0.73  (step t23 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (>= tptp.lambda1 1)) :rule and_pos)
% 0.50/0.73  (step t24 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule and_pos)
% 0.50/0.73  (step t25 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (>= tptp.mu1 0)) :rule and_pos)
% 0.50/0.73  (step t26 (cl false (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule resolution :premises (t22 t23 t24 t25))
% 0.50/0.73  (step t27 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) false) :rule reordering :premises (t26))
% 0.50/0.73  (step t28 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) false) :rule contraction :premises (t27))
% 0.50/0.73  (step t29 (cl (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) false) :rule resolution :premises (t21 t28))
% 0.50/0.73  (step t30 (cl (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (not false)) :rule implies_neg2)
% 0.50/0.73  (step t31 (cl (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false)) :rule resolution :premises (t29 t30))
% 0.50/0.73  (step t32 (cl (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false)) :rule contraction :premises (t31))
% 0.50/0.73  (step t33 (cl (= (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))))) :rule implies_simplify)
% 0.50/0.73  (step t34 (cl (not (=> (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false)) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule equiv1 :premises (t33))
% 0.50/0.73  (step t35 (cl (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule resolution :premises (t32 t34))
% 0.50/0.73  (step t36 (cl (= (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) false)) :rule resolution :premises (t20 t35))
% 0.50/0.73  (step t37 (cl (= (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) false))) :rule cong :premises (t16 t36))
% 0.50/0.73  (step t38 (cl (= (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) false) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))))) :rule all_simplify)
% 0.50/0.73  (step t39 (cl (= (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))))) :rule trans :premises (t37 t38))
% 0.50/0.73  (step t40 (cl (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t41)
% 0.50/0.73  (assume t41.a0 (>= tptp.mu1 0))
% 0.50/0.73  (assume t41.a1 (>= tptp.lambda1 1))
% 0.50/0.73  (assume t41.a2 (not (>= (+ tptp.mu1 tptp.lambda1) 1)))
% 0.50/0.73  (step t41.t1 (cl (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (not (>= tptp.mu1 0))) :rule and_neg)
% 0.50/0.73  (step t41.t2 (cl (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule resolution :premises (t41.t1 t41.a1 t41.a2 t41.a0))
% 0.50/0.73  (step t41 (cl (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.50/0.73  (step t42 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (>= tptp.mu1 0)) :rule and_pos)
% 0.50/0.73  (step t43 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (>= tptp.lambda1 1)) :rule and_pos)
% 0.50/0.73  (step t44 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule and_pos)
% 0.50/0.73  (step t45 (cl (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule resolution :premises (t41 t42 t43 t44))
% 0.50/0.73  (step t46 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule reordering :premises (t45))
% 0.50/0.73  (step t47 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule contraction :premises (t46))
% 0.50/0.73  (step t48 (cl (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) :rule resolution :premises (t40 t47))
% 0.50/0.73  (step t49 (cl (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (not (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule implies_neg2)
% 0.50/0.73  (step t50 (cl (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0))) (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule resolution :premises (t48 t49))
% 0.50/0.73  (step t51 (cl (=> (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))) (and (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (>= tptp.mu1 0)))) :rule contraction :premises (t50))
% 0.50/0.73  (step t52 (cl (not (and (>= tptp.mu1 0) (>= tptp.lambda1 1) (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule resolution :premises (t15 t39 t51))
% 0.50/0.73  (step t53 (cl (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule not_and :premises (t52))
% 0.50/0.73  (step t54 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (not (>= tptp.mu1 0)))) :rule or_neg)
% 0.50/0.73  (step t55 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (not (>= tptp.lambda1 1)))) :rule or_neg)
% 0.50/0.73  (step t56 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (not (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule or_neg)
% 0.50/0.73  (step t57 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule resolution :premises (t53 t54 t55 t56))
% 0.50/0.73  (step t58 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (not (not (>= (+ tptp.mu1 tptp.lambda1) 1))))) :rule contraction :premises (t57))
% 0.50/0.73  (step t59 (cl (or (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule resolution :premises (t1 t14 t58))
% 0.50/0.73  (step t60 (cl (not (>= tptp.mu1 0)) (not (>= tptp.lambda1 1)) (>= (+ tptp.mu1 tptp.lambda1) 1)) :rule or :premises (t59))
% 0.50/0.73  (step t61 (cl (not (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))) (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule or_pos)
% 0.50/0.73  (step t62 (cl (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (not (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))))) :rule reordering :premises (t61))
% 0.50/0.73  (step t63 (cl (not (= (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))))) (not (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01)))) :rule equiv_pos2)
% 0.50/0.73  (step t64 (cl (= (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))))) :rule refl)
% 0.50/0.73  (step t65 (cl (= (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01)))) :rule all_simplify)
% 0.50/0.73  (step t66 (cl (= (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))))) :rule cong :premises (t64 t65))
% 0.50/0.73  (step t67 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t68)
% 0.50/0.73  (assume t68.a0 (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))))
% 0.50/0.73  (step t68.t1 (cl (or (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)))) :rule forall_inst :args ((:= X tptp.x01)))
% 0.50/0.73  (step t68.t2 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) :rule or :premises (t68.t1))
% 0.50/0.73  (step t68.t3 (cl (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) :rule resolution :premises (t68.t2 t68.a0))
% 0.50/0.73  (step t68 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) :rule subproof :discharge (t68.a0))
% 0.50/0.73  (step t69 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) :rule resolution :premises (t67 t68))
% 0.50/0.73  (step t70 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (not (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)))) :rule implies_neg2)
% 0.50/0.73  (step t71 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)))) :rule resolution :premises (t69 t70))
% 0.50/0.73  (step t72 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 tptp.x01) (tptp.f1 tptp.x01)))) :rule contraction :premises (t71))
% 0.50/0.73  (step t73 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01)))) :rule resolution :premises (t63 t66 t72))
% 0.50/0.73  (step t74 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) :rule implies :premises (t73))
% 0.50/0.73  (step t75 (cl (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) :rule resolution :premises (t74 a10))
% 0.50/0.73  (step t76 (cl (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule and_neg)
% 0.50/0.73  (step t77 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t78)
% 0.50/0.73  (assume t78.a0 (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))
% 0.50/0.73  (assume t78.a1 (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))
% 0.50/0.73  (step t78.t1 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t78.t2)
% 0.50/0.73  (assume t78.t2.a0 (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))
% 0.50/0.73  (assume t78.t2.a1 (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))
% 0.50/0.73  (step t78.t2.t1 (cl (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule symm :premises (t78.t2.a1))
% 0.50/0.73  (step t78.t2.t2 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule symm :premises (t78.t2.t1))
% 0.50/0.73  (step t78.t2.t3 (cl (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule symm :premises (t78.t2.a0))
% 0.50/0.73  (step t78.t2.t4 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule trans :premises (t78.t2.t2 t78.t2.t3))
% 0.50/0.73  (step t78.t2 (cl (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule subproof :discharge (t78.t2.a0 t78.t2.a1))
% 0.50/0.73  (step t78.t3 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule and_pos)
% 0.50/0.73  (step t78.t4 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule and_pos)
% 0.50/0.73  (step t78.t5 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) :rule resolution :premises (t78.t2 t78.t3 t78.t4))
% 0.50/0.73  (step t78.t6 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule reordering :premises (t78.t5))
% 0.50/0.73  (step t78.t7 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule contraction :premises (t78.t6))
% 0.50/0.73  (step t78.t8 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule resolution :premises (t78.t1 t78.t7))
% 0.50/0.73  (step t78.t9 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule implies_neg2)
% 0.50/0.73  (step t78.t10 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule resolution :premises (t78.t8 t78.t9))
% 0.50/0.73  (step t78.t11 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule contraction :premises (t78.t10))
% 0.50/0.73  (step t78.t12 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule implies :premises (t78.t11))
% 0.50/0.73  (step t78.t13 (cl (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule and_neg)
% 0.50/0.73  (step t78.t14 (cl (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule resolution :premises (t78.t13 t78.a0 t78.a1))
% 0.50/0.73  (step t78.t15 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule resolution :premises (t78.t12 t78.t14))
% 0.50/0.73  (step t78 (cl (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule subproof :discharge (t78.a0 t78.a1))
% 0.50/0.73  (step t79 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule and_pos)
% 0.50/0.73  (step t80 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule and_pos)
% 0.50/0.73  (step t81 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) :rule resolution :premises (t78 t79 t80))
% 0.50/0.73  (step t82 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule reordering :premises (t81))
% 0.50/0.73  (step t83 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule contraction :premises (t82))
% 0.50/0.73  (step t84 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule resolution :premises (t77 t83))
% 0.50/0.73  (step t85 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule implies_neg2)
% 0.50/0.73  (step t86 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule resolution :premises (t84 t85))
% 0.50/0.73  (step t87 (cl (=> (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule contraction :premises (t86))
% 0.50/0.73  (step t88 (cl (not (and (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule implies :premises (t87))
% 0.50/0.73  (step t89 (cl (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule resolution :premises (t76 t88))
% 0.50/0.73  (step t90 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)) (not (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule reordering :premises (t89))
% 0.50/0.73  (step t91 (cl (not (= (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) (not (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))))) (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule equiv_pos2)
% 0.50/0.73  (step t92 (cl (= (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))) :rule refl)
% 0.50/0.73  (step t93 (cl (= (>= 2 1) true)) :rule all_simplify)
% 0.50/0.73  (step t94 (cl (= (not (>= 2 1)) (not true))) :rule cong :premises (t93))
% 0.50/0.73  (step t95 (cl (= (not true) false)) :rule all_simplify)
% 0.50/0.73  (step t96 (cl (= (not (>= 2 1)) false)) :rule trans :premises (t94 t95))
% 0.50/0.73  (step t97 (cl (= (tptp.iter1 2 tptp.x01) (tptp.iter1 2 tptp.x01))) :rule refl)
% 0.50/0.73  (step t98 (cl (= (+ (- 1) 2) 1)) :rule all_simplify)
% 0.50/0.73  (step t99 (cl (= (tptp.f1 tptp.x01) (tptp.f1 tptp.x01))) :rule refl)
% 0.50/0.73  (step t100 (cl (= (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule cong :premises (t98 t99))
% 0.50/0.73  (step t101 (cl (= (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule cong :premises (t97 t100))
% 0.50/0.73  (step t102 (cl (= (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))) (or false (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) :rule cong :premises (t96 t101))
% 0.50/0.73  (step t103 (cl (= (or false (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule all_simplify)
% 0.50/0.73  (step t104 (cl (= (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule trans :premises (t102 t103))
% 0.50/0.73  (step t105 (cl (= (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) :rule cong :premises (t92 t104))
% 0.50/0.73  (step t106 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t107)
% 0.50/0.73  (assume t107.a0 (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))
% 0.50/0.73  (step t107.t1 (cl (or (not (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))))) :rule forall_inst :args ((:= K 2) (:= X tptp.x01)))
% 0.50/0.73  (step t107.t2 (cl (not (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) :rule or :premises (t107.t1))
% 0.50/0.73  (step t107.t3 (cl (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) :rule resolution :premises (t107.t2 t107.a0))
% 0.50/0.73  (step t107 (cl (not (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) :rule subproof :discharge (t107.a0))
% 0.50/0.73  (step t108 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) :rule resolution :premises (t106 t107))
% 0.50/0.73  (step t109 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (not (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))))) :rule implies_neg2)
% 0.50/0.73  (step t110 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01))))) (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))))) :rule resolution :premises (t108 t109))
% 0.50/0.73  (step t111 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (or (not (>= 2 1)) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 (+ (- 1) 2) (tptp.f1 tptp.x01)))))) :rule contraction :premises (t110))
% 0.50/0.73  (step t112 (cl (=> (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule resolution :premises (t91 t105 t111))
% 0.50/0.73  (step t113 (cl (not (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule implies :premises (t112))
% 0.50/0.73  (step t114 (cl (not (= (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))) (not (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X)))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) :rule equiv_pos2)
% 0.50/0.73  (anchor :step t115 :args ((K Int) (:= K K) (X tptp.t1) (:= X X)))
% 0.50/0.73  (step t115.t1 (cl (= K K)) :rule refl)
% 0.50/0.73  (step t115.t2 (cl (= X X)) :rule refl)
% 0.50/0.73  (step t115.t3 (cl (= (< 0 K) (not (>= 0 K)))) :rule all_simplify)
% 0.50/0.73  (step t115.t4 (cl (= (>= 0 K) (not (>= K 1)))) :rule all_simplify)
% 0.50/0.73  (step t115.t5 (cl (= (not (>= 0 K)) (not (not (>= K 1))))) :rule cong :premises (t115.t4))
% 0.50/0.73  (step t115.t6 (cl (= (not (not (>= K 1))) (>= K 1))) :rule all_simplify)
% 0.50/0.73  (step t115.t7 (cl (= (not (>= 0 K)) (>= K 1))) :rule trans :premises (t115.t5 t115.t6))
% 0.50/0.73  (step t115.t8 (cl (= (< 0 K) (>= K 1))) :rule trans :premises (t115.t3 t115.t7))
% 0.50/0.73  (step t115.t9 (cl (= (tptp.iter1 K X) (tptp.iter1 K X))) :rule refl)
% 0.50/0.73  (step t115.t10 (cl (= (- K 1) (+ K (* (- 1) 1)))) :rule all_simplify)
% 0.50/0.73  (step t115.t11 (cl (= K K)) :rule refl)
% 0.50/0.73  (step t115.t12 (cl (= (* (- 1) 1) (- 1))) :rule all_simplify)
% 0.50/0.73  (step t115.t13 (cl (= (+ K (* (- 1) 1)) (+ K (- 1)))) :rule cong :premises (t115.t11 t115.t12))
% 0.50/0.73  (step t115.t14 (cl (= (+ K (- 1)) (+ (- 1) K))) :rule all_simplify)
% 0.50/0.73  (step t115.t15 (cl (= (+ K (* (- 1) 1)) (+ (- 1) K))) :rule trans :premises (t115.t13 t115.t14))
% 0.50/0.73  (step t115.t16 (cl (= (- K 1) (+ (- 1) K))) :rule trans :premises (t115.t10 t115.t15))
% 0.50/0.73  (step t115.t17 (cl (= (tptp.f1 X) (tptp.f1 X))) :rule refl)
% 0.50/0.73  (step t115.t18 (cl (= (tptp.iter1 (- K 1) (tptp.f1 X)) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))) :rule cong :premises (t115.t16 t115.t17))
% 0.50/0.73  (step t115.t19 (cl (= (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X))) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) :rule cong :premises (t115.t9 t115.t18))
% 0.50/0.73  (step t115.t20 (cl (= (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X)))) (=> (>= K 1) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) :rule cong :premises (t115.t8 t115.t19))
% 0.50/0.73  (step t115 (cl (= (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X))))) (forall ((K Int) (X tptp.t1)) (=> (>= K 1) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))) :rule bind)
% 0.50/0.73  (step t116 (cl (= (forall ((K Int) (X tptp.t1)) (=> (>= K 1) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))) :rule all_simplify)
% 0.50/0.73  (step t117 (cl (= (forall ((K Int) (X tptp.t1)) (=> (< 0 K) (= (tptp.iter1 K X) (tptp.iter1 (- K 1) (tptp.f1 X))))) (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X))))))) :rule trans :premises (t115 t116))
% 0.50/0.73  (step t118 (cl (forall ((K Int) (X tptp.t1)) (or (not (>= K 1)) (= (tptp.iter1 K X) (tptp.iter1 (+ (- 1) K) (tptp.f1 X)))))) :rule resolution :premises (t114 t117 a9))
% 0.50/0.73  (step t119 (cl (= (tptp.iter1 2 tptp.x01) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule resolution :premises (t113 t118))
% 0.50/0.73  (step t120 (cl (not (= (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) (not (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule equiv_pos2)
% 0.50/0.73  (step t121 (cl (= (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule all_simplify)
% 0.50/0.73  (step t122 (cl (= (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))))) :rule cong :premises (t64 t121))
% 0.50/0.73  (step t123 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t124)
% 0.50/0.73  (assume t124.a0 (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))))
% 0.50/0.73  (step t124.t1 (cl (or (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))))) :rule forall_inst :args ((:= X (tptp.f1 tptp.x01))))
% 0.50/0.73  (step t124.t2 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule or :premises (t124.t1))
% 0.50/0.73  (step t124.t3 (cl (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule resolution :premises (t124.t2 t124.a0))
% 0.50/0.73  (step t124 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule subproof :discharge (t124.a0))
% 0.50/0.73  (step t125 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule resolution :premises (t123 t124))
% 0.50/0.73  (step t126 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (not (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))))) :rule implies_neg2)
% 0.50/0.73  (step t127 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))))) :rule resolution :premises (t125 t126))
% 0.50/0.73  (step t128 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.iter1 1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01))))) :rule contraction :premises (t127))
% 0.50/0.73  (step t129 (cl (=> (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01))))) :rule resolution :premises (t120 t122 t128))
% 0.50/0.73  (step t130 (cl (not (forall ((X tptp.t1)) (= (tptp.iter1 1 X) (tptp.f1 X)))) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule implies :premises (t129))
% 0.50/0.73  (step t131 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 1 (tptp.f1 tptp.x01)))) :rule resolution :premises (t130 a10))
% 0.50/0.73  (step t132 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) :rule resolution :premises (t90 t119 t131))
% 0.50/0.73  (step t133 (cl (not (= (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))))) (not (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))))) :rule equiv_pos2)
% 0.50/0.73  (step t134 (cl (= (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) :rule refl)
% 0.50/0.73  (step t135 (cl (= (>= 1 1) true)) :rule all_simplify)
% 0.50/0.73  (step t136 (cl (= (not (>= 1 1)) (not true))) :rule cong :premises (t135))
% 0.50/0.73  (step t137 (cl (= (not (>= 1 1)) false)) :rule trans :premises (t136 t95))
% 0.50/0.73  (step t138 (cl (= tptp.mu1 tptp.mu1)) :rule refl)
% 0.50/0.73  (step t139 (cl (= tptp.lambda1 tptp.lambda1)) :rule refl)
% 0.50/0.73  (step t140 (cl (= (* (- 1) 1) (- 1))) :rule all_simplify)
% 0.50/0.73  (step t141 (cl (= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) (+ tptp.mu1 tptp.lambda1 (- 1)))) :rule cong :premises (t138 t139 t140))
% 0.50/0.73  (step t142 (cl (= (+ tptp.mu1 tptp.lambda1 (- 1)) (+ (- 1) tptp.mu1 tptp.lambda1))) :rule all_simplify)
% 0.50/0.73  (step t143 (cl (= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) (+ (- 1) tptp.mu1 tptp.lambda1))) :rule trans :premises (t141 t142))
% 0.50/0.73  (step t144 (cl (= 0 0)) :rule refl)
% 0.50/0.73  (step t145 (cl (= (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0) (>= (+ (- 1) tptp.mu1 tptp.lambda1) 0))) :rule cong :premises (t143 t144))
% 0.50/0.73  (step t146 (cl (= (>= (+ (- 1) tptp.mu1 tptp.lambda1) 0) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule all_simplify)
% 0.50/0.73  (step t147 (cl (= (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0) (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule trans :premises (t145 t146))
% 0.50/0.73  (step t148 (cl (= (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (>= (+ tptp.mu1 tptp.lambda1) 1)))) :rule cong :premises (t147))
% 0.50/0.73  (step t149 (cl (= (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))))) :rule refl)
% 0.50/0.73  (step t150 (cl (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.f1 (tptp.f1 tptp.x01)))) :rule refl)
% 0.50/0.73  (step t151 (cl (= (* 2 1) 2)) :rule all_simplify)
% 0.50/0.73  (step t152 (cl (= tptp.x01 tptp.x01)) :rule refl)
% 0.50/0.73  (step t153 (cl (= (tptp.iter1 (* 2 1) tptp.x01) (tptp.iter1 2 tptp.x01))) :rule cong :premises (t151 t152))
% 0.50/0.73  (step t154 (cl (= (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))) :rule cong :premises (t150 t153))
% 0.50/0.73  (step t155 (cl (= (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))) :rule cong :premises (t154))
% 0.50/0.73  (anchor :step t156 :args ((I Int) (:= I I)))
% 0.50/0.73  (step t156.t1 (cl (= I I)) :rule refl)
% 0.50/0.73  (step t156.t2 (cl (= (not (>= I 1)) (not (>= I 1)))) :rule refl)
% 0.50/0.73  (step t156.t3 (cl (= (>= (+ 1 (* (- 1) I)) 1) (not (>= I 1)))) :rule all_simplify)
% 0.50/0.73  (step t156.t4 (cl (= (not (>= (+ 1 (* (- 1) I)) 1)) (not (not (>= I 1))))) :rule cong :premises (t156.t3))
% 0.50/0.73  (step t156.t5 (cl (= (not (not (>= I 1))) (>= I 1))) :rule all_simplify)
% 0.50/0.73  (step t156.t6 (cl (= (not (>= (+ 1 (* (- 1) I)) 1)) (>= I 1))) :rule trans :premises (t156.t4 t156.t5))
% 0.50/0.73  (step t156.t7 (cl (= (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) :rule refl)
% 0.50/0.73  (step t156.t8 (cl (= (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))) (or (not (>= I 1)) (>= I 1) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))) :rule cong :premises (t156.t2 t156.t6 t156.t7))
% 0.50/0.73  (step t156 (cl (= (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) (forall ((I Int)) (or (not (>= I 1)) (>= I 1) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) :rule bind)
% 0.50/0.73  (step t157 (cl (= (forall ((I Int)) (or (not (>= I 1)) (>= I 1) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) (forall ((I Int)) true))) :rule all_simplify)
% 0.50/0.73  (step t158 (cl (= (forall ((I Int)) true) true)) :rule all_simplify)
% 0.50/0.73  (step t159 (cl (= (forall ((I Int)) (or (not (>= I 1)) (>= I 1) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) true)) :rule trans :premises (t157 t158))
% 0.50/0.73  (step t160 (cl (= (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) true)) :rule trans :premises (t156 t159))
% 0.50/0.73  (step t161 (cl (= (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))) (not true))) :rule cong :premises (t160))
% 0.50/0.73  (step t162 (cl (= (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))) false)) :rule trans :premises (t161 t95))
% 0.50/0.73  (step t163 (cl (= (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (or false (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) false))) :rule cong :premises (t137 t148 t149 t155 t162))
% 0.50/0.73  (step t164 (cl (= (or false (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))) false) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))))) :rule all_simplify)
% 0.50/0.73  (step t165 (cl (= (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))))) :rule trans :premises (t163 t164))
% 0.50/0.73  (step t166 (cl (= (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))))) :rule cong :premises (t134 t165))
% 0.50/0.73  (step t167 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule implies_neg1)
% 0.50/0.73  (anchor :step t168)
% 0.50/0.73  (assume t168.a0 (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))
% 0.50/0.73  (step t168.t1 (cl (or (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule forall_inst :args ((:= T 1)))
% 0.50/0.73  (step t168.t2 (cl (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) :rule or :premises (t168.t1))
% 0.50/0.73  (step t168.t3 (cl (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) :rule resolution :premises (t168.t2 t168.a0))
% 0.50/0.73  (step t168 (cl (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) :rule subproof :discharge (t168.a0))
% 0.50/0.73  (step t169 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) :rule resolution :premises (t167 t168))
% 0.50/0.73  (step t170 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (not (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule implies_neg2)
% 0.50/0.73  (step t171 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule resolution :premises (t169 t170))
% 0.50/0.73  (step t172 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= 1 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) 1)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 1) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ 1 (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule contraction :premises (t171))
% 0.50/0.73  (step t173 (cl (=> (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01)))))) :rule resolution :premises (t133 t166 t172))
% 0.50/0.73  (step t174 (cl (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))) :rule implies :premises (t173))
% 0.50/0.73  (step t175 (cl (not (= (not (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) (not (not (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule equiv_pos2)
% 0.50/0.73  (anchor :step t176 :args ((T Int) (:= T T)))
% 0.50/0.73  (step t176.t1 (cl (= T T)) :rule refl)
% 0.50/0.73  (step t176.t2 (cl (= (<= 1 T) (>= T 1))) :rule all_simplify)
% 0.50/0.73  (step t176.t3 (cl (= (<= T (+ tptp.mu1 tptp.lambda1)) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0))) :rule all_simplify)
% 0.50/0.73  (step t176.t4 (cl (= (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)))) :rule refl)
% 0.50/0.73  (step t176.t5 (cl (= (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)))) :rule refl)
% 0.50/0.73  (anchor :step t176.t6 :args ((I Int) (:= I I)))
% 0.50/0.73  (step t176.t6.t1 (cl (= I I)) :rule refl)
% 0.50/0.73  (step t176.t6.t2 (cl (= (<= 1 I) (>= I 1))) :rule all_simplify)
% 0.50/0.73  (step t176.t6.t3 (cl (= (< I T) (not (>= I T)))) :rule all_simplify)
% 0.50/0.73  (step t176.t6.t4 (cl (= (>= I T) (not (>= (+ T (* (- 1) I)) 1)))) :rule all_simplify)
% 0.50/0.73  (step t176.t6.t5 (cl (= (not (>= I T)) (not (not (>= (+ T (* (- 1) I)) 1))))) :rule cong :premises (t176.t6.t4))
% 0.50/0.73  (step t176.t6.t6 (cl (= (not (not (>= (+ T (* (- 1) I)) 1))) (>= (+ T (* (- 1) I)) 1))) :rule all_simplify)
% 0.50/0.73  (step t176.t6.t7 (cl (= (not (>= I T)) (>= (+ T (* (- 1) I)) 1))) :rule trans :premises (t176.t6.t5 t176.t6.t6))
% 0.50/0.73  (step t176.t6.t8 (cl (= (< I T) (>= (+ T (* (- 1) I)) 1))) :rule trans :premises (t176.t6.t3 t176.t6.t7))
% 0.50/0.73  (step t176.t6.t9 (cl (= (and (<= 1 I) (< I T)) (and (>= I 1) (>= (+ T (* (- 1) I)) 1)))) :rule cong :premises (t176.t6.t2 t176.t6.t8))
% 0.50/0.73  (step t176.t6.t10 (cl (= (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) :rule refl)
% 0.50/0.73  (step t176.t6.t11 (cl (= (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))) (=> (and (>= I 1) (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))) :rule cong :premises (t176.t6.t9 t176.t6.t10))
% 0.50/0.73  (step t176.t6 (cl (= (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) (forall ((I Int)) (=> (and (>= I 1) (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) :rule bind)
% 0.50/0.73  (step t176.t7 (cl (= (forall ((I Int)) (=> (and (>= I 1) (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) :rule all_simplify)
% 0.50/0.73  (step t176.t8 (cl (= (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) :rule trans :premises (t176.t6 t176.t7))
% 0.50/0.73  (step t176.t9 (cl (= (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))) (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) :rule cong :premises (t176.t2 t176.t3 t176.t4 t176.t5 t176.t8))
% 0.50/0.73  (step t176 (cl (= (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (exists ((T Int)) (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule bind)
% 0.50/0.73  (step t177 (cl (= (exists ((T Int)) (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (not (forall ((T Int)) (not (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))))) :rule all_simplify)
% 0.50/0.73  (step t178 (cl (= (forall ((T Int)) (not (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) :rule all_simplify)
% 0.50/0.73  (step t179 (cl (= (not (forall ((T Int)) (not (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))))) :rule cong :premises (t178))
% 0.50/0.73  (step t180 (cl (= (exists ((T Int)) (and (>= T 1) (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))))) :rule trans :premises (t177 t179))
% 0.50/0.73  (step t181 (cl (= (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))) (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))))) :rule trans :premises (t176 t180))
% 0.50/0.73  (step t182 (cl (= (not (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (not (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))))) :rule cong :premises (t181))
% 0.50/0.73  (step t183 (cl (= (not (not (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) :rule all_simplify)
% 0.50/0.73  (step t184 (cl (= (not (exists ((T Int)) (and (<= 1 T) (<= T (+ tptp.mu1 tptp.lambda1)) (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01)) (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01)) (forall ((I Int)) (=> (and (<= 1 I) (< I T)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))) (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01)))))))))) :rule trans :premises (t182 t183))
% 0.50/0.73  (step t185 (cl (forall ((T Int)) (or (not (>= T 1)) (not (>= (+ tptp.mu1 tptp.lambda1 (* (- 1) T)) 0)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 T tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 (* 2 T) tptp.x01))) (not (forall ((I Int)) (or (not (>= I 1)) (not (>= (+ T (* (- 1) I)) 1)) (not (= (tptp.iter1 I tptp.x01) (tptp.iter1 (* 2 I) tptp.x01))))))))) :rule resolution :premises (t175 t184 a23))
% 0.50/0.73  (step t186 (cl (or (not (>= (+ tptp.mu1 tptp.lambda1) 1)) (not (= (tptp.f1 tptp.x01) (tptp.iter1 1 tptp.x01))) (not (= (tptp.f1 (tptp.f1 tptp.x01)) (tptp.iter1 2 tptp.x01))))) :rule resolution :premises (t174 t185))
% 0.50/0.73  (step t187 (cl (not (>= (+ tptp.mu1 tptp.lambda1) 1))) :rule resolution :premises (t62 t75 t132 t186))
% 0.50/0.73  (step t188 (cl (not (= (<= 1 tptp.lambda1) (>= tptp.lambda1 1))) (not (<= 1 tptp.lambda1)) (>= tptp.lambda1 1)) :rule equiv_pos2)
% 0.50/0.73  (step t189 (cl (= (<= 1 tptp.lambda1) (>= tptp.lambda1 1))) :rule all_simplify)
% 0.50/0.73  (step t190 (cl (>= tptp.lambda1 1)) :rule resolution :premises (t188 t189 a13))
% 0.50/0.73  (step t191 (cl (not (= (<= 0 tptp.mu1) (>= tptp.mu1 0))) (not (<= 0 tptp.mu1)) (>= tptp.mu1 0)) :rule equiv_pos2)
% 0.50/0.73  (step t192 (cl (= (<= 0 tptp.mu1) (>= tptp.mu1 0))) :rule all_simplify)
% 0.50/0.73  (step t193 (cl (>= tptp.mu1 0)) :rule resolution :premises (t191 t192 a12))
% 0.50/0.73  (step t194 (cl) :rule resolution :premises (t60 t187 t190 t193))
% 0.50/0.73  
% 0.50/0.73  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.DMvtOlqnq7/cvc5---1.0.5_30082.smt2
% 0.50/0.73  % cvc5---1.0.5 exiting
% 0.50/0.73  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------