%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : DAT098_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n028.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 16:43:02 EDT 2024

% Result   : Theorem 0.20s 0.56s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT098_1 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 27 17:15:39 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_ARI
% 0.20/0.56  --- Run --finite-model-find --decision=internal at 15...
% 0.20/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.20/0.56  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.ss3TS0zWRq/cvc5---1.0.5_27091.smt2
% 0.20/0.56  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.ss3TS0zWRq/cvc5---1.0.5_27091.smt2
% 0.20/0.56  (assume a0 (forall ((K Int) (L tptp.list)) (= (tptp.head (tptp.cons K L)) K)))
% 0.20/0.56  (assume a1 (forall ((K Int) (L tptp.list)) (= (tptp.tail (tptp.cons K L)) L)))
% 0.20/0.56  (assume a2 (forall ((L tptp.list)) (or (= L tptp.nil) (= L (tptp.cons (tptp.head L) (tptp.tail L))))))
% 0.20/0.56  (assume a3 (forall ((K Int) (L tptp.list)) (not (= (tptp.cons K L) tptp.nil))))
% 0.20/0.56  (assume a4 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)))))))
% 0.20/0.56  (assume a5 (not (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))
% 0.20/0.56  (assume a6 true)
% 0.20/0.56  (step t1 (cl (not (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 tptp.nil))))) (not (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 tptp.nil)))) :rule equiv_pos2)
% 0.20/0.56  (step t2 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule refl)
% 0.20/0.56  (step t3 (cl (= (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil)) true)) :rule all_simplify)
% 0.20/0.56  (step t4 (cl (= (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not true))) :rule cong :premises (t3))
% 0.20/0.56  (step t5 (cl (= (not true) false)) :rule all_simplify)
% 0.20/0.56  (step t6 (cl (= (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) false)) :rule trans :premises (t4 t5))
% 0.20/0.56  (step t7 (cl (= (>= 2 0) true)) :rule all_simplify)
% 0.20/0.56  (step t8 (cl (= (not (>= 2 0)) (not true))) :rule cong :premises (t7))
% 0.20/0.56  (step t9 (cl (= (not (>= 2 0)) false)) :rule trans :premises (t8 t5))
% 0.20/0.56  (step t10 (cl (= (>= 2 4) false)) :rule all_simplify)
% 0.20/0.56  (step t11 (cl (= (not (tptp.inRange 4 tptp.nil)) (not (tptp.inRange 4 tptp.nil)))) :rule refl)
% 0.20/0.56  (step t12 (cl (= (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))) (or false false false (not (tptp.inRange 4 tptp.nil))))) :rule cong :premises (t6 t9 t10 t11))
% 0.20/0.56  (step t13 (cl (= (or false false false (not (tptp.inRange 4 tptp.nil))) (not (tptp.inRange 4 tptp.nil)))) :rule all_simplify)
% 0.20/0.56  (step t14 (cl (= (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))) (not (tptp.inRange 4 tptp.nil)))) :rule trans :premises (t12 t13))
% 0.20/0.56  (step t15 (cl (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 tptp.nil))))) :rule cong :premises (t2 t14))
% 0.20/0.56  (step t16 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t17)
% 0.20/0.56  (assume t17.a0 (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))
% 0.20/0.56  (step t17.t1 (cl (or (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))))) :rule forall_inst :args ((:= K 2) (:= T tptp.nil)))
% 0.20/0.56  (step t17.t2 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) :rule or :premises (t17.t1))
% 0.20/0.56  (step t17.t3 (cl (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) :rule resolution :premises (t17.t2 t17.a0))
% 0.20/0.56  (step t17 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) :rule subproof :discharge (t17.a0))
% 0.20/0.56  (step t18 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) :rule resolution :premises (t16 t17))
% 0.20/0.56  (step t19 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (not (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))))) :rule implies_neg2)
% 0.20/0.56  (step t20 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil)))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))))) :rule resolution :premises (t18 t19))
% 0.20/0.56  (step t21 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons 2 tptp.nil))) (not (>= 2 0)) (>= 2 4) (not (tptp.inRange 4 tptp.nil))))) :rule contraction :premises (t20))
% 0.20/0.56  (step t22 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 tptp.nil)))) :rule resolution :premises (t1 t15 t21))
% 0.20/0.56  (step t23 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (not (tptp.inRange 4 tptp.nil))) :rule implies :premises (t22))
% 0.20/0.56  (step t24 (cl (not (tptp.inRange 4 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule reordering :premises (t23))
% 0.20/0.56  (step t25 (cl (not (= (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv_pos2)
% 0.20/0.56  (step t26 (cl (= (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule refl)
% 0.20/0.56  (step t27 (cl (= (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule equiv_simplify)
% 0.20/0.56  (step t28 (cl (not (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv1 :premises (t27))
% 0.20/0.56  (step t29 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule all_simplify)
% 0.20/0.56  (step t30 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule all_simplify)
% 0.20/0.56  (step t31 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t2 t30))
% 0.20/0.56  (step t32 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule all_simplify)
% 0.20/0.56  (step t33 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) true)) :rule trans :premises (t31 t32))
% 0.20/0.56  (step t34 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule trans :premises (t29 t33))
% 0.20/0.56  (step t35 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t28 t34))
% 0.20/0.56  (step t36 (cl (= (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t26 t35))
% 0.20/0.56  (step t37 (cl (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule or_neg)
% 0.20/0.56  (step t38 (cl (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t39 (cl (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t40 (cl (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t37 t38 t39))
% 0.20/0.56  (step t41 (cl (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule contraction :premises (t40))
% 0.20/0.56  (step t42 (cl (or (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t25 t36 t41))
% 0.20/0.56  (step t43 (cl (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule or :premises (t42))
% 0.20/0.56  (step t44 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule reordering :premises (t43))
% 0.20/0.56  (step t45 (cl (not (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (not (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule equiv_pos1)
% 0.20/0.56  (step t46 (cl (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (not (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule reordering :premises (t45))
% 0.20/0.56  (step t47 (cl (not (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) (not (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule equiv_pos2)
% 0.20/0.56  (step t48 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule refl)
% 0.20/0.56  (step t49 (cl (= (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil))) true)) :rule all_simplify)
% 0.20/0.56  (step t50 (cl (= (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not true))) :rule cong :premises (t49))
% 0.20/0.56  (step t51 (cl (= (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) false)) :rule trans :premises (t50 t5))
% 0.20/0.56  (step t52 (cl (= (>= 3 0) true)) :rule all_simplify)
% 0.20/0.56  (step t53 (cl (= (not (>= 3 0)) (not true))) :rule cong :premises (t52))
% 0.20/0.56  (step t54 (cl (= (not (>= 3 0)) false)) :rule trans :premises (t53 t5))
% 0.20/0.56  (step t55 (cl (= (>= 3 4) false)) :rule all_simplify)
% 0.20/0.56  (step t56 (cl (= (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule refl)
% 0.20/0.56  (step t57 (cl (= (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) (or false false false (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule cong :premises (t51 t54 t55 t56))
% 0.20/0.56  (step t58 (cl (= (or false false false (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule all_simplify)
% 0.20/0.56  (step t59 (cl (= (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule trans :premises (t57 t58))
% 0.20/0.56  (step t60 (cl (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule cong :premises (t48 t59))
% 0.20/0.56  (step t61 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t62)
% 0.20/0.56  (assume t62.a0 (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))
% 0.20/0.56  (step t62.t1 (cl (or (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule forall_inst :args ((:= K 3) (:= T (tptp.cons 2 tptp.nil))))
% 0.20/0.56  (step t62.t2 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule or :premises (t62.t1))
% 0.20/0.56  (step t62.t3 (cl (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule resolution :premises (t62.t2 t62.a0))
% 0.20/0.56  (step t62 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule subproof :discharge (t62.a0))
% 0.20/0.56  (step t63 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule resolution :premises (t61 t62))
% 0.20/0.56  (step t64 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (not (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule implies_neg2)
% 0.20/0.56  (step t65 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule resolution :premises (t63 t64))
% 0.20/0.56  (step t66 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= 3 0)) (>= 3 4) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))))) :rule contraction :premises (t65))
% 0.20/0.56  (step t67 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))))) :rule resolution :premises (t47 t60 t66))
% 0.20/0.56  (step t68 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) :rule implies :premises (t67))
% 0.20/0.56  (step t69 (cl (not (tptp.inRange 4 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule reordering :premises (t68))
% 0.20/0.56  (step t70 (cl (not (= (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv_pos2)
% 0.20/0.56  (step t71 (cl (= (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule refl)
% 0.20/0.56  (step t72 (cl (= (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule equiv_simplify)
% 0.20/0.56  (step t73 (cl (not (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv1 :premises (t72))
% 0.20/0.56  (step t74 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule all_simplify)
% 0.20/0.56  (step t75 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule all_simplify)
% 0.20/0.56  (step t76 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t48 t75))
% 0.20/0.56  (step t77 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule all_simplify)
% 0.20/0.56  (step t78 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) true)) :rule trans :premises (t76 t77))
% 0.20/0.56  (step t79 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule trans :premises (t74 t78))
% 0.20/0.56  (step t80 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t73 t79))
% 0.20/0.56  (step t81 (cl (= (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t71 t80))
% 0.20/0.56  (step t82 (cl (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule or_neg)
% 0.20/0.56  (step t83 (cl (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t84 (cl (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t85 (cl (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t82 t83 t84))
% 0.20/0.56  (step t86 (cl (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule contraction :premises (t85))
% 0.20/0.56  (step t87 (cl (or (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t70 t81 t86))
% 0.20/0.56  (step t88 (cl (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule or :premises (t87))
% 0.20/0.56  (step t89 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule reordering :premises (t88))
% 0.20/0.56  (step t90 (cl (not (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule equiv_pos1)
% 0.20/0.56  (step t91 (cl (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule reordering :premises (t90))
% 0.20/0.56  (step t92 (cl (not (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) (not (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule equiv_pos2)
% 0.20/0.56  (step t93 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule refl)
% 0.20/0.56  (step t94 (cl (= (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) true)) :rule all_simplify)
% 0.20/0.56  (step t95 (cl (= (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not true))) :rule cong :premises (t94))
% 0.20/0.56  (step t96 (cl (= (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) false)) :rule trans :premises (t95 t5))
% 0.20/0.56  (step t97 (cl (= (>= 1 0) true)) :rule all_simplify)
% 0.20/0.56  (step t98 (cl (= (not (>= 1 0)) (not true))) :rule cong :premises (t97))
% 0.20/0.56  (step t99 (cl (= (not (>= 1 0)) false)) :rule trans :premises (t98 t5))
% 0.20/0.56  (step t100 (cl (= (>= 1 4) false)) :rule all_simplify)
% 0.20/0.56  (step t101 (cl (= (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule refl)
% 0.20/0.56  (step t102 (cl (= (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (or false false false (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule cong :premises (t96 t99 t100 t101))
% 0.20/0.56  (step t103 (cl (= (or false false false (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule all_simplify)
% 0.20/0.56  (step t104 (cl (= (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule trans :premises (t102 t103))
% 0.20/0.56  (step t105 (cl (= (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule cong :premises (t93 t104))
% 0.20/0.56  (step t106 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t107)
% 0.20/0.56  (assume t107.a0 (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))
% 0.20/0.56  (step t107.t1 (cl (or (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule forall_inst :args ((:= K 1) (:= T (tptp.cons 3 (tptp.cons 2 tptp.nil)))))
% 0.20/0.56  (step t107.t2 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule or :premises (t107.t1))
% 0.20/0.56  (step t107.t3 (cl (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule resolution :premises (t107.t2 t107.a0))
% 0.20/0.56  (step t107 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule subproof :discharge (t107.a0))
% 0.20/0.56  (step t108 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule resolution :premises (t106 t107))
% 0.20/0.56  (step t109 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (not (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule implies_neg2)
% 0.20/0.56  (step t110 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule resolution :premises (t108 t109))
% 0.20/0.56  (step t111 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= 1 0)) (>= 1 4) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule contraction :premises (t110))
% 0.20/0.56  (step t112 (cl (=> (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule resolution :premises (t92 t105 t111))
% 0.20/0.56  (step t113 (cl (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) :rule implies :premises (t112))
% 0.20/0.56  (step t114 (cl (not (= (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv_pos2)
% 0.20/0.56  (step t115 (cl (= (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule refl)
% 0.20/0.56  (step t116 (cl (= (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule equiv_simplify)
% 0.20/0.56  (step t117 (cl (not (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule equiv1 :premises (t116))
% 0.20/0.56  (step t118 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule all_simplify)
% 0.20/0.56  (step t119 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule all_simplify)
% 0.20/0.56  (step t120 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t93 t119))
% 0.20/0.56  (step t121 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule all_simplify)
% 0.20/0.56  (step t122 (cl (= (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) true)) :rule trans :premises (t120 t121))
% 0.20/0.56  (step t123 (cl (= (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) true)) :rule trans :premises (t118 t122))
% 0.20/0.56  (step t124 (cl (= (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t117 t123))
% 0.20/0.56  (step t125 (cl (= (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t115 t124))
% 0.20/0.56  (step t126 (cl (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule or_neg)
% 0.20/0.56  (step t127 (cl (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t128 (cl (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule or_neg)
% 0.20/0.56  (step t129 (cl (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t126 t127 t128))
% 0.20/0.56  (step t130 (cl (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (not (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule contraction :premises (t129))
% 0.20/0.56  (step t131 (cl (or (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule resolution :premises (t114 t125 t130))
% 0.20/0.56  (step t132 (cl (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule or :premises (t131))
% 0.20/0.56  (step t133 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule reordering :premises (t132))
% 0.20/0.56  (step t134 (cl (not (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule equiv_pos1)
% 0.20/0.56  (step t135 (cl (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) (not (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule reordering :premises (t134))
% 0.20/0.56  (step t136 (cl (not (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) (not (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule equiv_pos2)
% 0.20/0.56  (step t137 (cl (= (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))) :rule refl)
% 0.20/0.56  (step t138 (cl (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule refl)
% 0.20/0.56  (step t139 (cl (= (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule refl)
% 0.20/0.56  (anchor :step t140 :args ((K Int) (:= K K) (T tptp.list) (:= T T)))
% 0.20/0.56  (step t140.t1 (cl (= K K)) :rule refl)
% 0.20/0.56  (step t140.t2 (cl (= T T)) :rule refl)
% 0.20/0.56  (step t140.t3 (cl (= (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T)) (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule all_simplify)
% 0.20/0.56  (step t140.t4 (cl (= (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))) :rule cong :premises (t140.t3))
% 0.20/0.56  (step t140.t5 (cl (= (not (>= K 0)) (not (>= K 0)))) :rule refl)
% 0.20/0.56  (step t140.t6 (cl (= (>= (+ 4 (* (- 1) K)) 1) (not (>= K 4)))) :rule all_simplify)
% 0.20/0.56  (step t140.t7 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (not (not (>= K 4))))) :rule cong :premises (t140.t6))
% 0.20/0.56  (step t140.t8 (cl (= (not (not (>= K 4))) (>= K 4))) :rule all_simplify)
% 0.20/0.56  (step t140.t9 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (>= K 4))) :rule trans :premises (t140.t7 t140.t8))
% 0.20/0.56  (step t140.t10 (cl (= (not (tptp.inRange 4 T)) (not (tptp.inRange 4 T)))) :rule refl)
% 0.20/0.56  (step t140.t11 (cl (= (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule cong :premises (t140.t4 t140.t5 t140.t9 t140.t10))
% 0.20/0.56  (step t140 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule bind)
% 0.20/0.56  (step t141 (cl (= (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t140))
% 0.20/0.56  (step t142 (cl (= (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule cong :premises (t139 t141))
% 0.20/0.56  (step t143 (cl (= (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule cong :premises (t138 t142))
% 0.20/0.56  (step t144 (cl (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) :rule cong :premises (t137 t143))
% 0.20/0.56  (step t145 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t146)
% 0.20/0.56  (assume t146.a0 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))
% 0.20/0.56  (step t146.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule forall_inst :args ((:= N 4) (:= L (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))))
% 0.20/0.56  (step t146.t2 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule or :premises (t146.t1))
% 0.20/0.56  (step t146.t3 (cl (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t146.t2 t146.a0))
% 0.20/0.56  (step t146 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule subproof :discharge (t146.a0))
% 0.20/0.56  (step t147 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t145 t146))
% 0.20/0.56  (step t148 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (not (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule implies_neg2)
% 0.20/0.56  (step t149 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t147 t148))
% 0.20/0.56  (step t150 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule contraction :premises (t149))
% 0.20/0.56  (step t151 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t136 t144 t150))
% 0.20/0.56  (step t152 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule implies :premises (t151))
% 0.20/0.56  (step t153 (cl (not (= (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))) (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule equiv_pos2)
% 0.20/0.56  (anchor :step t154 :args ((N Int) (:= N N) (L tptp.list) (:= L L)))
% 0.20/0.56  (step t154.t1 (cl (= N N)) :rule refl)
% 0.20/0.56  (step t154.t2 (cl (= L L)) :rule refl)
% 0.20/0.56  (step t154.t3 (cl (= (tptp.inRange N L) (tptp.inRange N L))) :rule refl)
% 0.20/0.56  (step t154.t4 (cl (= (= L tptp.nil) (= tptp.nil L))) :rule all_simplify)
% 0.20/0.56  (anchor :step t154.t5 :args ((K Int) (:= K K) (T tptp.list) (:= T T)))
% 0.20/0.56  (step t154.t5.t1 (cl (= K K)) :rule refl)
% 0.20/0.56  (step t154.t5.t2 (cl (= T T)) :rule refl)
% 0.20/0.56  (step t154.t5.t3 (cl (= (= L (tptp.cons K T)) (= L (tptp.cons K T)))) :rule refl)
% 0.20/0.56  (step t154.t5.t4 (cl (= (<= 0 K) (>= K 0))) :rule all_simplify)
% 0.20/0.56  (step t154.t5.t5 (cl (= (< K N) (not (>= K N)))) :rule all_simplify)
% 0.20/0.56  (step t154.t5.t6 (cl (= (>= K N) (not (>= (+ N (* (- 1) K)) 1)))) :rule all_simplify)
% 0.20/0.56  (step t154.t5.t7 (cl (= (not (>= K N)) (not (not (>= (+ N (* (- 1) K)) 1))))) :rule cong :premises (t154.t5.t6))
% 0.20/0.56  (step t154.t5.t8 (cl (= (not (not (>= (+ N (* (- 1) K)) 1))) (>= (+ N (* (- 1) K)) 1))) :rule all_simplify)
% 0.20/0.56  (step t154.t5.t9 (cl (= (not (>= K N)) (>= (+ N (* (- 1) K)) 1))) :rule trans :premises (t154.t5.t7 t154.t5.t8))
% 0.20/0.56  (step t154.t5.t10 (cl (= (< K N) (>= (+ N (* (- 1) K)) 1))) :rule trans :premises (t154.t5.t5 t154.t5.t9))
% 0.20/0.56  (step t154.t5.t11 (cl (= (tptp.inRange N T) (tptp.inRange N T))) :rule refl)
% 0.20/0.56  (step t154.t5.t12 (cl (= (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)) (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T)))) :rule cong :premises (t154.t5.t3 t154.t5.t4 t154.t5.t10 t154.t5.t11))
% 0.20/0.56  (step t154.t5 (cl (= (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T))) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T))))) :rule bind)
% 0.20/0.56  (step t154.t6 (cl (= (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T))) (not (forall ((K Int) (T tptp.list)) (not (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T))))))) :rule all_simplify)
% 0.20/0.56  (step t154.t7 (cl (= (forall ((K Int) (T tptp.list)) (not (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T)))) (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))) :rule all_simplify)
% 0.20/0.56  (step t154.t8 (cl (= (not (forall ((K Int) (T tptp.list)) (not (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T))))) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))) :rule cong :premises (t154.t7))
% 0.20/0.56  (step t154.t9 (cl (= (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (>= K 0) (>= (+ N (* (- 1) K)) 1) (tptp.inRange N T))) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))) :rule trans :premises (t154.t6 t154.t8))
% 0.20/0.56  (step t154.t10 (cl (= (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T))) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))) :rule trans :premises (t154.t5 t154.t9))
% 0.20/0.56  (step t154.t11 (cl (= (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)))) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) :rule cong :premises (t154.t4 t154.t10))
% 0.20/0.56  (step t154.t12 (cl (= (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T))))) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule cong :premises (t154.t3 t154.t11))
% 0.20/0.56  (step t154 (cl (= (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= L tptp.nil) (exists ((K Int) (T tptp.list)) (and (= L (tptp.cons K T)) (<= 0 K) (< K N) (tptp.inRange N T)))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))) :rule bind)
% 0.20/0.56  (step t155 (cl (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule resolution :premises (t153 t154 a4))
% 0.20/0.56  (step t156 (cl (= (tptp.inRange 4 (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t152 t155))
% 0.20/0.56  (step t157 (cl (not (or (= tptp.nil (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t135 a5 t156))
% 0.20/0.56  (step t158 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 1 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule resolution :premises (t133 t157))
% 0.20/0.56  (step t159 (cl (not (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) :rule resolution :premises (t113 t158))
% 0.20/0.56  (step t160 (cl (not (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) (not (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule equiv_pos2)
% 0.20/0.56  (step t161 (cl (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))))) :rule refl)
% 0.20/0.56  (step t162 (cl (= (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))))) :rule refl)
% 0.20/0.56  (anchor :step t163 :args ((K Int) (:= K K) (T tptp.list) (:= T T)))
% 0.20/0.56  (step t163.t1 (cl (= K K)) :rule refl)
% 0.20/0.56  (step t163.t2 (cl (= T T)) :rule refl)
% 0.20/0.56  (step t163.t3 (cl (= (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T)) (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil))))) :rule all_simplify)
% 0.20/0.56  (step t163.t4 (cl (= (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))))) :rule cong :premises (t163.t3))
% 0.20/0.56  (step t163.t5 (cl (= (not (>= K 0)) (not (>= K 0)))) :rule refl)
% 0.20/0.56  (step t163.t6 (cl (= (>= (+ 4 (* (- 1) K)) 1) (not (>= K 4)))) :rule all_simplify)
% 0.20/0.56  (step t163.t7 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (not (not (>= K 4))))) :rule cong :premises (t163.t6))
% 0.20/0.56  (step t163.t8 (cl (= (not (not (>= K 4))) (>= K 4))) :rule all_simplify)
% 0.20/0.56  (step t163.t9 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (>= K 4))) :rule trans :premises (t163.t7 t163.t8))
% 0.20/0.56  (step t163.t10 (cl (= (not (tptp.inRange 4 T)) (not (tptp.inRange 4 T)))) :rule refl)
% 0.20/0.56  (step t163.t11 (cl (= (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule cong :premises (t163.t4 t163.t5 t163.t9 t163.t10))
% 0.20/0.56  (step t163 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule bind)
% 0.20/0.56  (step t164 (cl (= (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t163))
% 0.20/0.56  (step t165 (cl (= (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule cong :premises (t162 t164))
% 0.20/0.56  (step t166 (cl (= (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule cong :premises (t161 t165))
% 0.20/0.56  (step t167 (cl (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) :rule cong :premises (t137 t166))
% 0.20/0.56  (step t168 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t169)
% 0.20/0.56  (assume t169.a0 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))
% 0.20/0.56  (step t169.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule forall_inst :args ((:= N 4) (:= L (tptp.cons 3 (tptp.cons 2 tptp.nil)))))
% 0.20/0.56  (step t169.t2 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule or :premises (t169.t1))
% 0.20/0.56  (step t169.t3 (cl (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t169.t2 t169.a0))
% 0.20/0.56  (step t169 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule subproof :discharge (t169.a0))
% 0.20/0.56  (step t170 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t168 t169))
% 0.20/0.56  (step t171 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (not (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule implies_neg2)
% 0.20/0.56  (step t172 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t170 t171))
% 0.20/0.56  (step t173 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 3 (tptp.cons 2 tptp.nil)) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule contraction :premises (t172))
% 0.20/0.56  (step t174 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t160 t167 t173))
% 0.20/0.56  (step t175 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule implies :premises (t174))
% 0.20/0.56  (step t176 (cl (= (tptp.inRange 4 (tptp.cons 3 (tptp.cons 2 tptp.nil))) (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t175 t155))
% 0.20/0.56  (step t177 (cl (not (or (= tptp.nil (tptp.cons 3 (tptp.cons 2 tptp.nil))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t91 t159 t176))
% 0.20/0.56  (step t178 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 3 (tptp.cons 2 tptp.nil)))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule resolution :premises (t89 t177))
% 0.20/0.56  (step t179 (cl (not (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) :rule resolution :premises (t69 t178))
% 0.20/0.56  (step t180 (cl (not (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) (not (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule equiv_pos2)
% 0.20/0.56  (step t181 (cl (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (tptp.inRange 4 (tptp.cons 2 tptp.nil)))) :rule refl)
% 0.20/0.56  (step t182 (cl (= (= tptp.nil (tptp.cons 2 tptp.nil)) (= tptp.nil (tptp.cons 2 tptp.nil)))) :rule refl)
% 0.20/0.56  (anchor :step t183 :args ((K Int) (:= K K) (T tptp.list) (:= T T)))
% 0.20/0.56  (step t183.t1 (cl (= K K)) :rule refl)
% 0.20/0.56  (step t183.t2 (cl (= T T)) :rule refl)
% 0.20/0.56  (step t183.t3 (cl (= (= (tptp.cons 2 tptp.nil) (tptp.cons K T)) (= (tptp.cons K T) (tptp.cons 2 tptp.nil)))) :rule all_simplify)
% 0.20/0.56  (step t183.t4 (cl (= (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))))) :rule cong :premises (t183.t3))
% 0.20/0.56  (step t183.t5 (cl (= (not (>= K 0)) (not (>= K 0)))) :rule refl)
% 0.20/0.56  (step t183.t6 (cl (= (>= (+ 4 (* (- 1) K)) 1) (not (>= K 4)))) :rule all_simplify)
% 0.20/0.56  (step t183.t7 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (not (not (>= K 4))))) :rule cong :premises (t183.t6))
% 0.20/0.56  (step t183.t8 (cl (= (not (not (>= K 4))) (>= K 4))) :rule all_simplify)
% 0.20/0.56  (step t183.t9 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (>= K 4))) :rule trans :premises (t183.t7 t183.t8))
% 0.20/0.56  (step t183.t10 (cl (= (not (tptp.inRange 4 T)) (not (tptp.inRange 4 T)))) :rule refl)
% 0.20/0.56  (step t183.t11 (cl (= (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule cong :premises (t183.t4 t183.t5 t183.t9 t183.t10))
% 0.20/0.56  (step t183 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule bind)
% 0.20/0.56  (step t184 (cl (= (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t183))
% 0.20/0.56  (step t185 (cl (= (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule cong :premises (t182 t184))
% 0.20/0.56  (step t186 (cl (= (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule cong :premises (t181 t185))
% 0.20/0.56  (step t187 (cl (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))))) :rule cong :premises (t137 t186))
% 0.20/0.56  (step t188 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t189)
% 0.20/0.56  (assume t189.a0 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))
% 0.20/0.56  (step t189.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule forall_inst :args ((:= N 4) (:= L (tptp.cons 2 tptp.nil))))
% 0.20/0.56  (step t189.t2 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule or :premises (t189.t1))
% 0.20/0.56  (step t189.t3 (cl (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t189.t2 t189.a0))
% 0.20/0.56  (step t189 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule subproof :discharge (t189.a0))
% 0.20/0.56  (step t190 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t188 t189))
% 0.20/0.56  (step t191 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (not (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule implies_neg2)
% 0.20/0.56  (step t192 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t190 t191))
% 0.20/0.56  (step t193 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons 2 tptp.nil) (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule contraction :premises (t192))
% 0.20/0.56  (step t194 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t180 t187 t193))
% 0.20/0.56  (step t195 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule implies :premises (t194))
% 0.20/0.56  (step t196 (cl (= (tptp.inRange 4 (tptp.cons 2 tptp.nil)) (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t195 t155))
% 0.20/0.56  (step t197 (cl (not (or (= tptp.nil (tptp.cons 2 tptp.nil)) (not (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t46 t179 t196))
% 0.20/0.56  (step t198 (cl (forall ((K Int) (T tptp.list)) (or (not (= (tptp.cons K T) (tptp.cons 2 tptp.nil))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule resolution :premises (t44 t197))
% 0.20/0.56  (step t199 (cl (not (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (tptp.inRange 4 tptp.nil)))) (not (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (tptp.inRange 4 tptp.nil))) :rule equiv_pos2)
% 0.20/0.56  (step t200 (cl (= (tptp.inRange 4 tptp.nil) (tptp.inRange 4 tptp.nil))) :rule refl)
% 0.20/0.56  (step t201 (cl (= (= tptp.nil tptp.nil) true)) :rule all_simplify)
% 0.20/0.56  (anchor :step t202 :args ((K Int) (:= K K) (T tptp.list) (:= T T)))
% 0.20/0.56  (step t202.t1 (cl (= K K)) :rule refl)
% 0.20/0.56  (step t202.t2 (cl (= T T)) :rule refl)
% 0.20/0.56  (step t202.t3 (cl (= (not (= tptp.nil (tptp.cons K T))) (not (= tptp.nil (tptp.cons K T))))) :rule refl)
% 0.20/0.56  (step t202.t4 (cl (= (not (>= K 0)) (not (>= K 0)))) :rule refl)
% 0.20/0.56  (step t202.t5 (cl (= (>= (+ 4 (* (- 1) K)) 1) (not (>= K 4)))) :rule all_simplify)
% 0.20/0.56  (step t202.t6 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (not (not (>= K 4))))) :rule cong :premises (t202.t5))
% 0.20/0.56  (step t202.t7 (cl (= (not (not (>= K 4))) (>= K 4))) :rule all_simplify)
% 0.20/0.56  (step t202.t8 (cl (= (not (>= (+ 4 (* (- 1) K)) 1)) (>= K 4))) :rule trans :premises (t202.t6 t202.t7))
% 0.20/0.56  (step t202.t9 (cl (= (not (tptp.inRange 4 T)) (not (tptp.inRange 4 T)))) :rule refl)
% 0.20/0.56  (step t202.t10 (cl (= (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))) :rule cong :premises (t202.t3 t202.t4 t202.t8 t202.t9))
% 0.20/0.56  (step t202 (cl (= (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))) (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) :rule bind)
% 0.20/0.56  (step t203 (cl (= (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T))))))) :rule cong :premises (t202))
% 0.20/0.56  (step t204 (cl (= (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))) (or true (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))))) :rule cong :premises (t201 t203))
% 0.20/0.56  (step t205 (cl (= (or true (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (>= K 4) (not (tptp.inRange 4 T)))))) true)) :rule all_simplify)
% 0.20/0.56  (step t206 (cl (= (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))) true)) :rule trans :premises (t204 t205))
% 0.20/0.56  (step t207 (cl (= (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))) (= (tptp.inRange 4 tptp.nil) true))) :rule cong :premises (t200 t206))
% 0.20/0.56  (step t208 (cl (= (= (tptp.inRange 4 tptp.nil) true) (tptp.inRange 4 tptp.nil))) :rule all_simplify)
% 0.20/0.56  (step t209 (cl (= (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))) (tptp.inRange 4 tptp.nil))) :rule trans :premises (t207 t208))
% 0.20/0.56  (step t210 (cl (= (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (tptp.inRange 4 tptp.nil)))) :rule cong :premises (t137 t209))
% 0.20/0.56  (step t211 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) :rule implies_neg1)
% 0.20/0.56  (anchor :step t212)
% 0.20/0.56  (assume t212.a0 (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))))
% 0.20/0.56  (step t212.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule forall_inst :args ((:= N 4) (:= L tptp.nil)))
% 0.20/0.56  (step t212.t2 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule or :premises (t212.t1))
% 0.20/0.56  (step t212.t3 (cl (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t212.t2 t212.a0))
% 0.20/0.56  (step t212 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule subproof :discharge (t212.a0))
% 0.20/0.56  (step t213 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) :rule resolution :premises (t211 t212))
% 0.20/0.56  (step t214 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (not (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule implies_neg2)
% 0.20/0.56  (step t215 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T)))))))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule resolution :premises (t213 t214))
% 0.20/0.56  (step t216 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (= (tptp.inRange 4 tptp.nil) (or (= tptp.nil tptp.nil) (not (forall ((K Int) (T tptp.list)) (or (not (= tptp.nil (tptp.cons K T))) (not (>= K 0)) (not (>= (+ 4 (* (- 1) K)) 1)) (not (tptp.inRange 4 T))))))))) :rule contraction :premises (t215))
% 0.20/0.56  (step t217 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T)))))))) (tptp.inRange 4 tptp.nil))) :rule resolution :premises (t199 t210 t216))
% 0.20/0.56  (step t218 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.inRange N L) (or (= tptp.nil L) (not (forall ((K Int) (T tptp.list)) (or (not (= L (tptp.cons K T))) (not (>= K 0)) (not (>= (+ N (* (- 1) K)) 1)) (not (tptp.inRange N T))))))))) (tptp.inRange 4 tptp.nil)) :rule implies :premises (t217))
% 0.20/0.56  (step t219 (cl (tptp.inRange 4 tptp.nil)) :rule resolution :premises (t218 t155))
% 0.20/0.56  (step t220 (cl) :rule resolution :premises (t24 t198 t219))
% 0.20/0.56  
% 0.20/0.56  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.ss3TS0zWRq/cvc5---1.0.5_27091.smt2
% 0.20/0.56  % cvc5---1.0.5 exiting
% 0.20/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------