TSTP Solution File: DAT089_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : DAT089_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n023.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 16:43:00 EDT 2024
% Result : Theorem 15.75s 16.02s
% Output : Proof 15.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : DAT089_1 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 27 17:20:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 15.75/16.02 --- Run --finite-model-find --decision=internal at 15...
% 15.75/16.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.75/16.02 --- Run --no-e-matching --full-saturate-quant at 15...
% 15.75/16.02 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.2qaNs8rJ3X/cvc5---1.0.5_3832.smt2
% 15.75/16.02 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.2qaNs8rJ3X/cvc5---1.0.5_3832.smt2
% 15.75/16.02 (assume a0 (forall ((K Int) (L tptp.list)) (= (tptp.head (tptp.cons K L)) K)))
% 15.75/16.02 (assume a1 (forall ((K Int) (L tptp.list)) (= (tptp.tail (tptp.cons K L)) L)))
% 15.75/16.02 (assume a2 (forall ((L tptp.list)) (or (= L tptp.nil) (= L (tptp.cons (tptp.head L) (tptp.tail L))))))
% 15.75/16.02 (assume a3 (forall ((K Int) (L tptp.list)) (not (= (tptp.cons K L) tptp.nil))))
% 15.75/16.02 (assume a4 (forall ((X Int) (L tptp.list)) (= (tptp.in X L) (or (exists ((H Int) (T tptp.list)) (and (= L (tptp.cons H T)) (= X H))) (exists ((H Int) (T tptp.list)) (and (= L (tptp.cons H T)) (tptp.in X T)))))))
% 15.75/16.02 (assume a5 (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)))))))
% 15.75/16.02 (assume a6 (= (tptp.length tptp.nil) 0))
% 15.75/16.02 (assume a7 (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))))
% 15.75/16.02 (assume a8 (forall ((K Int)) (= (tptp.count K tptp.nil) 0)))
% 15.75/16.02 (assume a9 (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))
% 15.75/16.02 (assume a10 (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (= K H) (= (tptp.count K (tptp.cons H T)) (+ (tptp.count K T) 1)))))
% 15.75/16.02 (assume a11 (forall ((L tptp.list)) (= (tptp.append tptp.nil L) L)))
% 15.75/16.02 (assume a12 (forall ((I Int) (K tptp.list) (L tptp.list)) (= (tptp.append (tptp.cons I K) L) (tptp.cons I (tptp.append K L)))))
% 15.75/16.02 (assume a13 (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0))))
% 15.75/16.02 (assume a14 (not (not (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))))))
% 15.75/16.02 (assume a15 true)
% 15.75/16.02 (step t1 (cl (not (= (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule equiv_pos2)
% 15.75/16.02 (step t2 (cl (= (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) 0)))) :rule refl)
% 15.75/16.02 (step t3 (cl (= (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule refl)
% 15.75/16.02 (step t4 (cl (= (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)))) :rule refl)
% 15.75/16.02 (step t5 (cl (= (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule refl)
% 15.75/16.02 (step t6 (cl (= (= (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) true) (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule equiv_simplify)
% 15.75/16.02 (step t7 (cl (not (= (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) true)) (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule equiv1 :premises (t6))
% 15.75/16.02 (step t8 (cl (= (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule all_simplify)
% 15.75/16.02 (step t9 (cl (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule refl)
% 15.75/16.02 (step t10 (cl (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule all_simplify)
% 15.75/16.02 (step t11 (cl (= (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule cong :premises (t9 t10))
% 15.75/16.02 (step t12 (cl (= (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) true)) :rule all_simplify)
% 15.75/16.02 (step t13 (cl (= (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) true)) :rule trans :premises (t11 t12))
% 15.75/16.02 (step t14 (cl (= (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) true)) :rule trans :premises (t8 t13))
% 15.75/16.02 (step t15 (cl (= (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t7 t14))
% 15.75/16.02 (step t16 (cl (= (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule cong :premises (t2 t3 t4 t5 t15))
% 15.75/16.02 (step t17 (cl (not (= (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) (not (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule equiv_pos2)
% 15.75/16.02 (step t18 (cl (= (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule refl)
% 15.75/16.02 (step t19 (cl (= (= (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule equiv_simplify)
% 15.75/16.02 (step t20 (cl (= (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (not (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule equiv2 :premises (t19))
% 15.75/16.02 (step t21 (cl (not (not (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule not_not)
% 15.75/16.02 (step t22 (cl (= (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule resolution :premises (t20 t21))
% 15.75/16.02 (step t23 (cl (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t24)
% 15.75/16.02 (assume t24.a0 (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))
% 15.75/16.02 (assume t24.a1 (= (tptp.length tptp.nil) 0))
% 15.75/16.02 (assume t24.a2 (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (assume t24.a3 (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))
% 15.75/16.02 (step t24.t1 (cl (not (= (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule equiv_pos2)
% 15.75/16.02 (step t24.t2 (cl (= (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule all_simplify)
% 15.75/16.02 (step t24.t3 (cl (= (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule symm :premises (t24.t2))
% 15.75/16.02 (step t24.t4 (cl (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule resolution :premises (t24.t1 t24.t3 t24.a3))
% 15.75/16.02 (step t24.t5 (cl (not (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule equiv_pos2)
% 15.75/16.02 (step t24.t6 (cl (= (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule cong :premises (t24.t2))
% 15.75/16.02 (step t24.t7 (cl (= (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule trans :premises (t24.t6 t10))
% 15.75/16.02 (step t24.t8 (cl (= (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule symm :premises (t24.t7))
% 15.75/16.02 (step t24.t9 (cl (not (= (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (not (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule equiv_pos2)
% 15.75/16.02 (step t24.t10 (cl (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule implies_neg1)
% 15.75/16.02 (anchor :step t24.t11)
% 15.75/16.02 (assume t24.t11.a0 (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))
% 15.75/16.02 (step t24.t11.t1 (cl (not (= (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0))) false)) (not (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))) false) :rule equiv_pos2)
% 15.75/16.02 (step t24.t11.t2 (cl (= (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0))) (not (>= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t3 (cl (= (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (to_real (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t4 (cl (= (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (to_real (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t5 (cl (= (* (- 1.0) (tptp.length tptp.nil)) (to_real (* (- 1) (tptp.length tptp.nil))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t6 (cl (= (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (to_real (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t7 (cl (= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (to_real (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (to_real (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (to_real (* (- 1) (tptp.length tptp.nil))) (to_real (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule cong :premises (t24.t11.t3 t24.t11.t4 t24.t11.t5 t24.t11.t6))
% 15.75/16.02 (step t24.t11.t8 (cl (= (+ (to_real (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (to_real (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (to_real (* (- 1) (tptp.length tptp.nil))) (to_real (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 0.0)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t9 (cl (= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 0.0)) :rule trans :premises (t24.t11.t7 t24.t11.t8))
% 15.75/16.02 (step t24.t11.t10 (cl (= (* 1.0 1) 1.0)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t11 (cl (= (* 1.0 (- 1)) (- 1.0))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t12 (cl (= (* (- 1.0) 0) 0.0)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t13 (cl (= (* 1.0 0) 0.0)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t14 (cl (= (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)) (+ 1.0 (- 1.0) 0.0 0.0))) :rule cong :premises (t24.t11.t10 t24.t11.t11 t24.t11.t12 t24.t11.t13))
% 15.75/16.02 (step t24.t11.t15 (cl (= (+ 1.0 (- 1.0) 0.0 0.0) 0.0)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t16 (cl (= (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)) 0.0)) :rule trans :premises (t24.t11.t14 t24.t11.t15))
% 15.75/16.02 (step t24.t11.t17 (cl (= (>= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0))) (>= 0.0 0.0))) :rule cong :premises (t24.t11.t9 t24.t11.t16))
% 15.75/16.02 (step t24.t11.t18 (cl (= (>= 0.0 0.0) true)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t19 (cl (= (>= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0))) true)) :rule trans :premises (t24.t11.t17 t24.t11.t18))
% 15.75/16.02 (step t24.t11.t20 (cl (= (not (>= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))) (not true))) :rule cong :premises (t24.t11.t19))
% 15.75/16.02 (step t24.t11.t21 (cl (= (not true) false)) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t22 (cl (= (not (>= (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))) false)) :rule trans :premises (t24.t11.t20 t24.t11.t21))
% 15.75/16.02 (step t24.t11.t23 (cl (= (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0))) false)) :rule trans :premises (t24.t11.t2 t24.t11.t22))
% 15.75/16.02 (step t24.t11.t24 (cl (not (< (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 1))) (not (= (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1.0 (- 1)))) (not (= (* (- 1.0) (tptp.length tptp.nil)) (* (- 1.0) 0))) (not (= (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (* 1.0 0))) (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))) :rule la_generic :args (1 (- 1) (- 1) (- 1) 1))
% 15.75/16.02 (step t24.t11.t25 (cl (=> (and (> 1.0 0) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (< (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 1)))) :rule la_mult_pos)
% 15.75/16.02 (step t24.t11.t26 (cl (not (and (> 1.0 0) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (< (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 1))) :rule implies :premises (t24.t11.t25))
% 15.75/16.02 (step t24.t11.t27 (cl (and (> 1.0 0) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) (not (> 1.0 0)) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule and_neg)
% 15.75/16.02 (step t24.t11.t28 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 15.75/16.02 (step t24.t11.t29 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t24.t11.t28))
% 15.75/16.02 (step t24.t11.t30 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 15.75/16.02 (step t24.t11.t31 (cl (> 1.0 0)) :rule resolution :premises (t24.t11.t29 t24.t11.t30))
% 15.75/16.02 (step t24.t11.t32 (cl (and (> 1.0 0) (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t24.t11.t27 t24.t11.t31 t24.t11.a0))
% 15.75/16.02 (step t24.t11.t33 (cl (< (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 1))) :rule resolution :premises (t24.t11.t26 t24.t11.t32))
% 15.75/16.02 (step t24.t11.t34 (cl (=> (and (> 1.0 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) (= (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1.0 (- 1))))) :rule la_mult_pos)
% 15.75/16.02 (step t24.t11.t35 (cl (not (and (> 1.0 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) (= (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1.0 (- 1)))) :rule implies :premises (t24.t11.t34))
% 15.75/16.02 (step t24.t11.t36 (cl (and (> 1.0 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) (not (> 1.0 0)) (not (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule and_neg)
% 15.75/16.02 (step t24.t11.t37 (cl (not (= (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) :rule equiv_pos2)
% 15.75/16.02 (step t24.t11.t38 (cl (= (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule all_simplify)
% 15.75/16.02 (step t24.t11.t39 (cl (= (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule symm :premises (t24.t11.t38))
% 15.75/16.02 (step t24.t11.t40 (cl (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) :rule resolution :premises (t24.t11.t37 t24.t11.t39 t24.a2))
% 15.75/16.02 (step t24.t11.t41 (cl (and (> 1.0 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule resolution :premises (t24.t11.t36 t24.t11.t31 t24.t11.t40))
% 15.75/16.02 (step t24.t11.t42 (cl (= (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1.0 (- 1)))) :rule resolution :premises (t24.t11.t35 t24.t11.t41))
% 15.75/16.02 (step t24.t11.t43 (cl (=> (and (< (- 1.0) 0) (= (tptp.length tptp.nil) 0)) (= (* (- 1.0) (tptp.length tptp.nil)) (* (- 1.0) 0)))) :rule la_mult_neg)
% 15.75/16.02 (step t24.t11.t44 (cl (not (and (< (- 1.0) 0) (= (tptp.length tptp.nil) 0))) (= (* (- 1.0) (tptp.length tptp.nil)) (* (- 1.0) 0))) :rule implies :premises (t24.t11.t43))
% 15.75/16.02 (step t24.t11.t45 (cl (and (< (- 1.0) 0) (= (tptp.length tptp.nil) 0)) (not (< (- 1.0) 0)) (not (= (tptp.length tptp.nil) 0))) :rule and_neg)
% 15.75/16.02 (step t24.t11.t46 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 15.75/16.02 (step t24.t11.t47 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t24.t11.t46))
% 15.75/16.02 (step t24.t11.t48 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 15.75/16.02 (step t24.t11.t49 (cl (< (- 1.0) 0)) :rule resolution :premises (t24.t11.t47 t24.t11.t48))
% 15.75/16.02 (step t24.t11.t50 (cl (and (< (- 1.0) 0) (= (tptp.length tptp.nil) 0))) :rule resolution :premises (t24.t11.t45 t24.t11.t49 t24.a1))
% 15.75/16.02 (step t24.t11.t51 (cl (= (* (- 1.0) (tptp.length tptp.nil)) (* (- 1.0) 0))) :rule resolution :premises (t24.t11.t44 t24.t11.t50))
% 15.75/16.02 (step t24.t11.t52 (cl (=> (and (> 1.0 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0)) (= (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (* 1.0 0)))) :rule la_mult_pos)
% 15.75/16.02 (step t24.t11.t53 (cl (not (and (> 1.0 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0))) (= (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (* 1.0 0))) :rule implies :premises (t24.t11.t52))
% 15.75/16.02 (step t24.t11.t54 (cl (and (> 1.0 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0)) (not (> 1.0 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0))) :rule and_neg)
% 15.75/16.02 (step t24.t11.t55 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0)) :rule symm :premises (t24.a0))
% 15.75/16.02 (step t24.t11.t56 (cl (and (> 1.0 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t24.t11.t54 t24.t11.t31 t24.t11.t55))
% 15.75/16.02 (step t24.t11.t57 (cl (= (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (* 1.0 0))) :rule resolution :premises (t24.t11.t53 t24.t11.t56))
% 15.75/16.02 (step t24.t11.t58 (cl (< (+ (* 1.0 (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (* 1.0 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1.0) (tptp.length tptp.nil)) (* 1.0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (+ (* 1.0 1) (* 1.0 (- 1)) (* (- 1.0) 0) (* 1.0 0)))) :rule resolution :premises (t24.t11.t24 t24.t11.t33 t24.t11.t42 t24.t11.t51 t24.t11.t57))
% 15.75/16.02 (step t24.t11.t59 (cl false) :rule resolution :premises (t24.t11.t1 t24.t11.t23 t24.t11.t58))
% 15.75/16.02 (step t24.t11 (cl (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) false) :rule subproof :discharge (t24.t11.a0))
% 15.75/16.02 (step t24.t12 (cl (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false) false) :rule resolution :premises (t24.t10 t24.t11))
% 15.75/16.02 (step t24.t13 (cl (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false) (not false)) :rule implies_neg2)
% 15.75/16.02 (step t24.t14 (cl (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false) (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false)) :rule resolution :premises (t24.t12 t24.t13))
% 15.75/16.02 (step t24.t15 (cl (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false)) :rule contraction :premises (t24.t14))
% 15.75/16.02 (step t24.t16 (cl (= (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule implies_simplify)
% 15.75/16.02 (step t24.t17 (cl (not (=> (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) false)) (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule equiv1 :premises (t24.t16))
% 15.75/16.02 (step t24.t18 (cl (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t24.t15 t24.t17))
% 15.75/16.02 (step t24.t19 (cl (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule resolution :premises (t24.t9 t24.t7 t24.t18))
% 15.75/16.02 (step t24.t20 (cl (not (< (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t24.t5 t24.t8 t24.t19))
% 15.75/16.02 (step t24.t21 (cl) :rule resolution :premises (t24.t4 t24.t20))
% 15.75/16.02 (step t24 (cl (not (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) :rule subproof :discharge (t24.a0 t24.a1 t24.a2 t24.a3))
% 15.75/16.02 (step t25 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule and_pos)
% 15.75/16.02 (step t26 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.length tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t27 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule and_pos)
% 15.75/16.02 (step t28 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule and_pos)
% 15.75/16.02 (step t29 (cl false (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t24 t25 t26 t27 t28))
% 15.75/16.02 (step t30 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) false) :rule reordering :premises (t29))
% 15.75/16.02 (step t31 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) false) :rule contraction :premises (t30))
% 15.75/16.02 (step t32 (cl (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) false) :rule resolution :premises (t23 t31))
% 15.75/16.02 (step t33 (cl (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (not false)) :rule implies_neg2)
% 15.75/16.02 (step t34 (cl (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false)) :rule resolution :premises (t32 t33))
% 15.75/16.02 (step t35 (cl (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false)) :rule contraction :premises (t34))
% 15.75/16.02 (step t36 (cl (= (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule implies_simplify)
% 15.75/16.02 (step t37 (cl (not (=> (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false)) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule equiv1 :premises (t36))
% 15.75/16.02 (step t38 (cl (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t35 t37))
% 15.75/16.02 (step t39 (cl (= (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false)) :rule resolution :premises (t22 t38))
% 15.75/16.02 (step t40 (cl (= (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false))) :rule cong :premises (t18 t39))
% 15.75/16.02 (step t41 (cl (= (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) false) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule all_simplify)
% 15.75/16.02 (step t42 (cl (= (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))))) :rule trans :premises (t40 t41))
% 15.75/16.02 (step t43 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t44)
% 15.75/16.02 (assume t44.a0 (= (tptp.length tptp.nil) 0))
% 15.75/16.02 (assume t44.a1 (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (assume t44.a2 (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))
% 15.75/16.02 (assume t44.a3 (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))
% 15.75/16.02 (assume t44.a4 (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))
% 15.75/16.02 (step t44.t1 (cl (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (not (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule and_neg)
% 15.75/16.02 (step t44.t2 (cl (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t44.t3)
% 15.75/16.02 (assume t44.t3.a0 (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))
% 15.75/16.02 (assume t44.t3.a1 (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))
% 15.75/16.02 (step t44.t3.t1 (cl (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))) :rule symm :premises (t44.t3.a1))
% 15.75/16.02 (step t44.t3.t2 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))) :rule symm :premises (t44.t3.a0))
% 15.75/16.02 (step t44.t3.t3 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule symm :premises (t44.t3.t2))
% 15.75/16.02 (step t44.t3.t4 (cl (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule trans :premises (t44.t3.t1 t44.t3.t3))
% 15.75/16.02 (step t44.t3 (cl (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule subproof :discharge (t44.t3.a0 t44.t3.a1))
% 15.75/16.02 (step t44.t4 (cl (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule and_pos)
% 15.75/16.02 (step t44.t5 (cl (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t44.t6 (cl (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)))) :rule resolution :premises (t44.t3 t44.t4 t44.t5))
% 15.75/16.02 (step t44.t7 (cl (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule reordering :premises (t44.t6))
% 15.75/16.02 (step t44.t8 (cl (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule contraction :premises (t44.t7))
% 15.75/16.02 (step t44.t9 (cl (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule resolution :premises (t44.t2 t44.t8))
% 15.75/16.02 (step t44.t10 (cl (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule implies_neg2)
% 15.75/16.02 (step t44.t11 (cl (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t44.t9 t44.t10))
% 15.75/16.02 (step t44.t12 (cl (=> (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule contraction :premises (t44.t11))
% 15.75/16.02 (step t44.t13 (cl (not (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule implies :premises (t44.t12))
% 15.75/16.02 (step t44.t14 (cl (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule and_neg)
% 15.75/16.02 (step t44.t15 (cl (and (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule resolution :premises (t44.t14 t44.a3 t44.a2))
% 15.75/16.02 (step t44.t16 (cl (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule resolution :premises (t44.t13 t44.t15))
% 15.75/16.02 (step t44.t17 (cl (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule resolution :premises (t44.t1 t44.t16 t44.a0 t44.a1 t44.a4))
% 15.75/16.02 (step t44 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule subproof :discharge (t44.a0 t44.a1 t44.a2 t44.a3 t44.a4))
% 15.75/16.02 (step t45 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.length tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t46 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule and_pos)
% 15.75/16.02 (step t47 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t48 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule and_pos)
% 15.75/16.02 (step t49 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule and_pos)
% 15.75/16.02 (step t50 (cl (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t44 t45 t46 t47 t48 t49))
% 15.75/16.02 (step t51 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule reordering :premises (t50))
% 15.75/16.02 (step t52 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule contraction :premises (t51))
% 15.75/16.02 (step t53 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule resolution :premises (t43 t52))
% 15.75/16.02 (step t54 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule implies_neg2)
% 15.75/16.02 (step t55 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t53 t54))
% 15.75/16.02 (step t56 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) (and (= 0 (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule contraction :premises (t55))
% 15.75/16.02 (step t57 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t17 t42 t56))
% 15.75/16.02 (step t58 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule not_and :premises (t57))
% 15.75/16.02 (step t59 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (not (= (tptp.length tptp.nil) 0)))) :rule or_neg)
% 15.75/16.02 (step t60 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule or_neg)
% 15.75/16.02 (step t61 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)))) :rule or_neg)
% 15.75/16.02 (step t62 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule or_neg)
% 15.75/16.02 (step t63 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (not (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule or_neg)
% 15.75/16.02 (step t64 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule resolution :premises (t58 t59 t60 t61 t62 t63))
% 15.75/16.02 (step t65 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (not (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule contraction :premises (t64))
% 15.75/16.02 (step t66 (cl (or (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t1 t16 t65))
% 15.75/16.02 (step t67 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)) :rule or :premises (t66))
% 15.75/16.02 (step t68 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule reordering :premises (t67))
% 15.75/16.02 (step t69 (cl (not (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule or_pos)
% 15.75/16.02 (step t70 (cl (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) (not (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule reordering :premises (t69))
% 15.75/16.02 (step t71 (cl (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule and_neg)
% 15.75/16.02 (step t72 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t73)
% 15.75/16.02 (assume t73.a0 (= (tptp.length tptp.nil) 0))
% 15.75/16.02 (assume t73.a1 (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (step t73.t1 (cl (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t73.t2)
% 15.75/16.02 (assume t73.t2.a0 (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (step t73.t2.t1 (cl (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule not_symm :premises (t73.t2.a0))
% 15.75/16.02 (step t73.t2 (cl (not (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule subproof :discharge (t73.t2.a0))
% 15.75/16.02 (step t73.t3 (cl (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t73.t1 t73.t2))
% 15.75/16.02 (step t73.t4 (cl (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (not (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule implies_neg2)
% 15.75/16.02 (step t73.t5 (cl (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule resolution :premises (t73.t3 t73.t4))
% 15.75/16.02 (step t73.t6 (cl (=> (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule contraction :premises (t73.t5))
% 15.75/16.02 (step t73.t7 (cl (not (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule implies :premises (t73.t6))
% 15.75/16.02 (step t73.t8 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t73.t9)
% 15.75/16.02 (assume t73.t9.a0 (= (tptp.length tptp.nil) 0))
% 15.75/16.02 (assume t73.t9.a1 (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (step t73.t9.t1 (cl (= (= (= 0 (tptp.length (tptp.cons 0 tptp.nil))) false) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))))) :rule equiv_simplify)
% 15.75/16.02 (step t73.t9.t2 (cl (not (= (= 0 (tptp.length (tptp.cons 0 tptp.nil))) false)) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule equiv1 :premises (t73.t9.t1))
% 15.75/16.02 (step t73.t9.t3 (cl (= 0 (tptp.length tptp.nil))) :rule symm :premises (t73.t9.a0))
% 15.75/16.02 (step t73.t9.t4 (cl (= (tptp.length (tptp.cons 0 tptp.nil)) (tptp.length (tptp.cons 0 tptp.nil)))) :rule refl)
% 15.75/16.02 (step t73.t9.t5 (cl (= (= 0 (tptp.length (tptp.cons 0 tptp.nil))) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) :rule cong :premises (t73.t9.t3 t73.t9.t4))
% 15.75/16.02 (step t73.t9.t6 (cl (= (= (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule equiv_simplify)
% 15.75/16.02 (step t73.t9.t7 (cl (= (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (not (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule equiv2 :premises (t73.t9.t6))
% 15.75/16.02 (step t73.t9.t8 (cl (not (not (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))))) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) :rule not_not)
% 15.75/16.02 (step t73.t9.t9 (cl (= (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) :rule resolution :premises (t73.t9.t7 t73.t9.t8))
% 15.75/16.02 (step t73.t9.t10 (cl (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t73.t9.t11)
% 15.75/16.02 (assume t73.t9.t11.a0 (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))
% 15.75/16.02 (step t73.t9.t11.t1 (cl (not (= (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1)))) false)) (not (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1))))) false) :rule equiv_pos2)
% 15.75/16.02 (step t73.t9.t11.t2 (cl (= (* (- 1) (tptp.length tptp.nil)) (* (- 1) (tptp.length tptp.nil)))) :rule refl)
% 15.75/16.02 (step t73.t9.t11.t3 (cl (= (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t4 (cl (= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length tptp.nil)) (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule cong :premises (t73.t9.t11.t2 t73.t9.t11.t3))
% 15.75/16.02 (step t73.t9.t11.t5 (cl (= (+ (* (- 1) (tptp.length tptp.nil)) (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t6 (cl (= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule trans :premises (t73.t9.t11.t4 t73.t9.t11.t5))
% 15.75/16.02 (step t73.t9.t11.t7 (cl (= (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule refl)
% 15.75/16.02 (step t73.t9.t11.t8 (cl (= (* 1 (- 1)) (- 1))) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t9 (cl (= (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (- 1)))) :rule cong :premises (t73.t9.t11.t7 t73.t9.t11.t8))
% 15.75/16.02 (step t73.t9.t11.t10 (cl (= (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (- 1)) (+ (- 1) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t11 (cl (= (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1))) (+ (- 1) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule trans :premises (t73.t9.t11.t9 t73.t9.t11.t10))
% 15.75/16.02 (step t73.t9.t11.t12 (cl (= (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1)))) (<= (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (+ (- 1) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule cong :premises (t73.t9.t11.t6 t73.t9.t11.t11))
% 15.75/16.02 (step t73.t9.t11.t13 (cl (= (<= (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (+ (- 1) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) false)) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t14 (cl (= (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1)))) false)) :rule trans :premises (t73.t9.t11.t12 t73.t9.t11.t13))
% 15.75/16.02 (step t73.t9.t11.t15 (cl (not (= (* (- 1) (tptp.length tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1 (- 1)))) (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1))))) :rule la_generic :args ((- 1) (- 1) 1))
% 15.75/16.02 (step t73.t9.t11.t16 (cl (=> (and (< (- 1) 0) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) (= (* (- 1) (tptp.length tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule la_mult_neg)
% 15.75/16.02 (step t73.t9.t11.t17 (cl (not (and (< (- 1) 0) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) (= (* (- 1) (tptp.length tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule implies :premises (t73.t9.t11.t16))
% 15.75/16.02 (step t73.t9.t11.t18 (cl (and (< (- 1) 0) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) (not (< (- 1) 0)) (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) :rule and_neg)
% 15.75/16.02 (step t73.t9.t11.t19 (cl (= (= (< (- 1) 0) true) (< (- 1) 0))) :rule equiv_simplify)
% 15.75/16.02 (step t73.t9.t11.t20 (cl (not (= (< (- 1) 0) true)) (< (- 1) 0)) :rule equiv1 :premises (t73.t9.t11.t19))
% 15.75/16.02 (step t73.t9.t11.t21 (cl (= (< (- 1) 0) true)) :rule hole :args ((< (- 1) 0)))
% 15.75/16.02 (step t73.t9.t11.t22 (cl (< (- 1) 0)) :rule resolution :premises (t73.t9.t11.t20 t73.t9.t11.t21))
% 15.75/16.02 (step t73.t9.t11.t23 (cl (and (< (- 1) 0) (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t9.t11.t18 t73.t9.t11.t22 t73.t9.t11.a0))
% 15.75/16.02 (step t73.t9.t11.t24 (cl (= (* (- 1) (tptp.length tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t9.t11.t17 t73.t9.t11.t23))
% 15.75/16.02 (step t73.t9.t11.t25 (cl (=> (and (> 1 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) (= (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1 (- 1))))) :rule la_mult_pos)
% 15.75/16.02 (step t73.t9.t11.t26 (cl (not (and (> 1 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) (= (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1 (- 1)))) :rule implies :premises (t73.t9.t11.t25))
% 15.75/16.02 (step t73.t9.t11.t27 (cl (and (> 1 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) (not (> 1 0)) (not (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule and_neg)
% 15.75/16.02 (step t73.t9.t11.t28 (cl (= (= (> 1 0) true) (> 1 0))) :rule equiv_simplify)
% 15.75/16.02 (step t73.t9.t11.t29 (cl (not (= (> 1 0) true)) (> 1 0)) :rule equiv1 :premises (t73.t9.t11.t28))
% 15.75/16.02 (step t73.t9.t11.t30 (cl (= (> 1 0) true)) :rule hole :args ((> 1 0)))
% 15.75/16.02 (step t73.t9.t11.t31 (cl (> 1 0)) :rule resolution :premises (t73.t9.t11.t29 t73.t9.t11.t30))
% 15.75/16.02 (step t73.t9.t11.t32 (cl (not (= (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) :rule equiv_pos2)
% 15.75/16.02 (step t73.t9.t11.t33 (cl (= (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule all_simplify)
% 15.75/16.02 (step t73.t9.t11.t34 (cl (= (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule symm :premises (t73.t9.t11.t33))
% 15.75/16.02 (step t73.t9.t11.t35 (cl (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1))) :rule resolution :premises (t73.t9.t11.t32 t73.t9.t11.t34 t73.t9.a1))
% 15.75/16.02 (step t73.t9.t11.t36 (cl (and (> 1 0) (= (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (- 1)))) :rule resolution :premises (t73.t9.t11.t27 t73.t9.t11.t31 t73.t9.t11.t35))
% 15.75/16.02 (step t73.t9.t11.t37 (cl (= (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (* 1 (- 1)))) :rule resolution :premises (t73.t9.t11.t26 t73.t9.t11.t36))
% 15.75/16.02 (step t73.t9.t11.t38 (cl (<= (+ (* (- 1) (tptp.length tptp.nil)) (* 1 (+ (tptp.length tptp.nil) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (* 1 (- 1))))) :rule resolution :premises (t73.t9.t11.t15 t73.t9.t11.t24 t73.t9.t11.t37))
% 15.75/16.02 (step t73.t9.t11.t39 (cl false) :rule resolution :premises (t73.t9.t11.t1 t73.t9.t11.t14 t73.t9.t11.t38))
% 15.75/16.02 (step t73.t9.t11 (cl (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))) false) :rule subproof :discharge (t73.t9.t11.a0))
% 15.75/16.02 (step t73.t9.t12 (cl (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) false) :rule resolution :premises (t73.t9.t10 t73.t9.t11))
% 15.75/16.02 (step t73.t9.t13 (cl (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (not false)) :rule implies_neg2)
% 15.75/16.02 (step t73.t9.t14 (cl (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false)) :rule resolution :premises (t73.t9.t12 t73.t9.t13))
% 15.75/16.02 (step t73.t9.t15 (cl (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false)) :rule contraction :premises (t73.t9.t14))
% 15.75/16.02 (step t73.t9.t16 (cl (= (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false) (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule implies_simplify)
% 15.75/16.02 (step t73.t9.t17 (cl (not (=> (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false)) (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) :rule equiv1 :premises (t73.t9.t16))
% 15.75/16.02 (step t73.t9.t18 (cl (not (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t9.t15 t73.t9.t17))
% 15.75/16.02 (step t73.t9.t19 (cl (= (= (tptp.length tptp.nil) (tptp.length (tptp.cons 0 tptp.nil))) false)) :rule resolution :premises (t73.t9.t9 t73.t9.t18))
% 15.75/16.02 (step t73.t9.t20 (cl (= (= 0 (tptp.length (tptp.cons 0 tptp.nil))) false)) :rule trans :premises (t73.t9.t5 t73.t9.t19))
% 15.75/16.02 (step t73.t9.t21 (cl (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t9.t2 t73.t9.t20))
% 15.75/16.02 (step t73.t9 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule subproof :discharge (t73.t9.a0 t73.t9.a1))
% 15.75/16.02 (step t73.t10 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (= (tptp.length tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t73.t11 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule and_pos)
% 15.75/16.02 (step t73.t12 (cl (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule resolution :premises (t73.t9 t73.t10 t73.t11))
% 15.75/16.02 (step t73.t13 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule reordering :premises (t73.t12))
% 15.75/16.02 (step t73.t14 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule contraction :premises (t73.t13))
% 15.75/16.02 (step t73.t15 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t8 t73.t14))
% 15.75/16.02 (step t73.t16 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (not (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))))) :rule implies_neg2)
% 15.75/16.02 (step t73.t17 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))))) :rule resolution :premises (t73.t15 t73.t16))
% 15.75/16.02 (step t73.t18 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil)))))) :rule contraction :premises (t73.t17))
% 15.75/16.02 (step t73.t19 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule implies :premises (t73.t18))
% 15.75/16.02 (step t73.t20 (cl (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule and_neg)
% 15.75/16.02 (step t73.t21 (cl (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule resolution :premises (t73.t20 t73.a0 t73.a1))
% 15.75/16.02 (step t73.t22 (cl (not (= 0 (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t73.t19 t73.t21))
% 15.75/16.02 (step t73.t23 (cl (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t73.t7 t73.t22))
% 15.75/16.02 (step t73 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule subproof :discharge (t73.a0 t73.a1))
% 15.75/16.02 (step t74 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (= (tptp.length tptp.nil) 0)) :rule and_pos)
% 15.75/16.02 (step t75 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule and_pos)
% 15.75/16.02 (step t76 (cl (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule resolution :premises (t73 t74 t75))
% 15.75/16.02 (step t77 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule reordering :premises (t76))
% 15.75/16.02 (step t78 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule contraction :premises (t77))
% 15.75/16.02 (step t79 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t72 t78))
% 15.75/16.02 (step t80 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (not (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule implies_neg2)
% 15.75/16.02 (step t81 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule resolution :premises (t79 t80))
% 15.75/16.02 (step t82 (cl (=> (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0)))) :rule contraction :premises (t81))
% 15.75/16.02 (step t83 (cl (not (and (= (tptp.length tptp.nil) 0) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule implies :premises (t82))
% 15.75/16.02 (step t84 (cl (not (= (tptp.length tptp.nil) 0)) (not (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t71 t83))
% 15.75/16.02 (step t85 (cl (not (= (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) (not (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))))) (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule equiv_pos2)
% 15.75/16.02 (step t86 (cl (= (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))))) :rule refl)
% 15.75/16.02 (step t87 (cl (= (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule all_simplify)
% 15.75/16.02 (step t88 (cl (= (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))))) :rule cong :premises (t86 t87))
% 15.75/16.02 (step t89 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T))))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t90)
% 15.75/16.02 (assume t90.a0 (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))))
% 15.75/16.02 (step t90.t1 (cl (or (not (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T))))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))))) :rule forall_inst :args ((:= H 0) (:= T tptp.nil)))
% 15.75/16.02 (step t90.t2 (cl (not (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T))))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) :rule or :premises (t90.t1))
% 15.75/16.02 (step t90.t3 (cl (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) :rule resolution :premises (t90.t2 t90.a0))
% 15.75/16.02 (step t90 (cl (not (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T))))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) :rule subproof :discharge (t90.a0))
% 15.75/16.02 (step t91 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) :rule resolution :premises (t89 t90))
% 15.75/16.02 (step t92 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (not (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))))) :rule implies_neg2)
% 15.75/16.02 (step t93 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil)))) (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))))) :rule resolution :premises (t91 t92))
% 15.75/16.02 (step t94 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length (tptp.cons 0 tptp.nil)) (+ 1 (tptp.length tptp.nil))))) :rule contraction :premises (t93))
% 15.75/16.02 (step t95 (cl (=> (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil)))))) :rule resolution :premises (t85 t88 t94))
% 15.75/16.02 (step t96 (cl (not (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T))))) (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule implies :premises (t95))
% 15.75/16.02 (step t97 (cl (= (tptp.length tptp.nil) (+ (- 1) (tptp.length (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t96 a7))
% 15.75/16.02 (step t98 (cl (not (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule resolution :premises (t84 a6 t97))
% 15.75/16.02 (step t99 (cl (not (= (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))))) (not (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule equiv_pos2)
% 15.75/16.02 (step t100 (cl (= (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))) :rule refl)
% 15.75/16.02 (step t101 (cl (= (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.length (tptp.cons 0 tptp.nil)) 0))) :rule refl)
% 15.75/16.02 (step t102 (cl (= (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule all_simplify)
% 15.75/16.02 (step t103 (cl (= (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule cong :premises (t101 t102))
% 15.75/16.02 (step t104 (cl (= (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))))) :rule cong :premises (t100 t103))
% 15.75/16.02 (step t105 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t106)
% 15.75/16.02 (assume t106.a0 (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))
% 15.75/16.02 (step t106.t1 (cl (or (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))))) :rule forall_inst :args ((:= K (tptp.length (tptp.cons 0 tptp.nil))) (:= H 0) (:= T tptp.nil)))
% 15.75/16.02 (step t106.t2 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) :rule or :premises (t106.t1))
% 15.75/16.02 (step t106.t3 (cl (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) :rule resolution :premises (t106.t2 t106.a0))
% 15.75/16.02 (step t106 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) :rule subproof :discharge (t106.a0))
% 15.75/16.02 (step t107 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) :rule resolution :premises (t105 t106))
% 15.75/16.02 (step t108 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (not (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))))) :rule implies_neg2)
% 15.75/16.02 (step t109 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil)))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))))) :rule resolution :premises (t107 t108))
% 15.75/16.02 (step t110 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil))))) :rule contraction :premises (t109))
% 15.75/16.02 (step t111 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))))) :rule resolution :premises (t99 t104 t110))
% 15.75/16.02 (step t112 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule implies :premises (t111))
% 15.75/16.02 (step t113 (cl (not (= (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))) (not (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) :rule equiv_pos2)
% 15.75/16.02 (step t114 (cl (= (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (forall ((K Int) (H Int) (T tptp.list) (N Int)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))) :rule all_simplify)
% 15.75/16.02 (step t115 (cl (= (forall ((K Int) (H Int) (T tptp.list) (N Int)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))) :rule all_simplify)
% 15.75/16.02 (step t116 (cl (= (forall ((K Int) (H Int) (T tptp.list) (N Int)) (=> (not (= K H)) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))) :rule trans :premises (t114 t115))
% 15.75/16.02 (step t117 (cl (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) :rule resolution :premises (t113 t116 a9))
% 15.75/16.02 (step t118 (cl (or (= (tptp.length (tptp.cons 0 tptp.nil)) 0) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule resolution :premises (t112 t117))
% 15.75/16.02 (step t119 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) :rule resolution :premises (t70 t98 t118))
% 15.75/16.02 (step t120 (cl (not (= (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) (not (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0))) (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule equiv_pos2)
% 15.75/16.02 (step t121 (cl (= (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)))) :rule refl)
% 15.75/16.02 (step t122 (cl (= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))))) :rule all_simplify)
% 15.75/16.02 (step t123 (cl (= 0 0)) :rule refl)
% 15.75/16.02 (step t124 (cl (= (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0) (>= (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) 0))) :rule cong :premises (t122 t123))
% 15.75/16.02 (step t125 (cl (= (>= (+ (* (- 1) (tptp.length (tptp.cons 0 tptp.nil))) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil))) 0) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule all_simplify)
% 15.75/16.02 (step t126 (cl (= (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule trans :premises (t124 t125))
% 15.75/16.02 (step t127 (cl (= (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))))) :rule cong :premises (t121 t126))
% 15.75/16.02 (step t128 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t129)
% 15.75/16.02 (assume t129.a0 (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)))
% 15.75/16.02 (step t129.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0))) :rule forall_inst :args ((:= N (tptp.length (tptp.cons 0 tptp.nil))) (:= L (tptp.cons 0 tptp.nil))))
% 15.75/16.02 (step t129.t2 (cl (not (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) :rule or :premises (t129.t1))
% 15.75/16.02 (step t129.t3 (cl (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) :rule resolution :premises (t129.t2 t129.a0))
% 15.75/16.02 (step t129 (cl (not (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) :rule subproof :discharge (t129.a0))
% 15.75/16.02 (step t130 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) :rule resolution :premises (t128 t129))
% 15.75/16.02 (step t131 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (not (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0))) :rule implies_neg2)
% 15.75/16.02 (step t132 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0)) (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0))) :rule resolution :premises (t130 t131))
% 15.75/16.02 (step t133 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (>= (+ (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.length (tptp.cons 0 tptp.nil)))) 0))) :rule contraction :premises (t132))
% 15.75/16.02 (step t134 (cl (=> (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1)))) :rule resolution :premises (t120 t127 t133))
% 15.75/16.02 (step t135 (cl (not (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule implies :premises (t134))
% 15.75/16.02 (step t136 (cl (not (= (not (not (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))))) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)))) (not (not (not (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L)))))) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) :rule equiv_pos2)
% 15.75/16.02 (step t137 (cl (= (not (not (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))))) (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))))) :rule all_simplify)
% 15.75/16.02 (anchor :step t138 :args ((N Int) (:= N N) (L tptp.list) (:= L L)))
% 15.75/16.02 (step t138.t1 (cl (= N N)) :rule refl)
% 15.75/16.02 (step t138.t2 (cl (= L L)) :rule refl)
% 15.75/16.02 (step t138.t3 (cl (= (>= (tptp.count N L) (tptp.length L)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) :rule all_simplify)
% 15.75/16.02 (step t138 (cl (= (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)))) :rule bind)
% 15.75/16.02 (step t139 (cl (= (not (not (forall ((N Int) (L tptp.list)) (>= (tptp.count N L) (tptp.length L))))) (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0)))) :rule trans :premises (t137 t138))
% 15.75/16.02 (step t140 (cl (forall ((N Int) (L tptp.list)) (>= (+ (tptp.count N L) (* (- 1) (tptp.length L))) 0))) :rule resolution :premises (t136 t139 a14))
% 15.75/16.02 (step t141 (cl (not (>= (+ (tptp.length (tptp.cons 0 tptp.nil)) (* (- 1) (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) (tptp.cons 0 tptp.nil)))) 1))) :rule resolution :premises (t135 t140))
% 15.75/16.02 (step t142 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) :rule implies_neg1)
% 15.75/16.02 (anchor :step t143)
% 15.75/16.02 (assume t143.a0 (forall ((K Int)) (= (tptp.count K tptp.nil) 0)))
% 15.75/16.02 (step t143.t1 (cl (or (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule forall_inst :args ((:= K (tptp.length (tptp.cons 0 tptp.nil)))))
% 15.75/16.02 (step t143.t2 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule or :premises (t143.t1))
% 15.75/16.02 (step t143.t3 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule resolution :premises (t143.t2 t143.a0))
% 15.75/16.02 (step t143 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule subproof :discharge (t143.a0))
% 15.75/16.02 (step t144 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule resolution :premises (t142 t143))
% 15.75/16.02 (step t145 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (not (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule implies_neg2)
% 15.75/16.02 (step t146 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule resolution :premises (t144 t145))
% 15.75/16.02 (step t147 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0))) :rule contraction :premises (t146))
% 15.75/16.02 (step t148 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule implies :premises (t147))
% 15.75/16.02 (step t149 (cl (= (tptp.count (tptp.length (tptp.cons 0 tptp.nil)) tptp.nil) 0)) :rule resolution :premises (t148 a8))
% 15.75/16.02 (step t150 (cl) :rule resolution :premises (t68 t119 t141 t149 t97 a6))
% 15.75/16.02
% 15.75/16.02 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.2qaNs8rJ3X/cvc5---1.0.5_3832.smt2
% 15.75/16.02 % cvc5---1.0.5 exiting
% 15.75/16.02 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------