TSTP Solution File: DAT080_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : DAT080_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n015.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 16:42:59 EDT 2024
% Result : Theorem 0.76s 0.95s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT080_1 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 17:15:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_ARI
% 0.76/0.95 --- Run --finite-model-find --decision=internal at 15...
% 0.76/0.95 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.FQcW4yfAWz/cvc5---1.0.5_5189.smt2
% 0.76/0.95 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.FQcW4yfAWz/cvc5---1.0.5_5189.smt2
% 0.76/0.95 (assume a0 (forall ((K Int) (L tptp.list)) (= (tptp.head (tptp.cons K L)) K)))
% 0.76/0.95 (assume a1 (forall ((K Int) (L tptp.list)) (= (tptp.tail (tptp.cons K L)) L)))
% 0.76/0.95 (assume a2 (forall ((L tptp.list)) (or (= L tptp.nil) (= L (tptp.cons (tptp.head L) (tptp.tail L))))))
% 0.76/0.95 (assume a3 (forall ((K Int) (L tptp.list)) (not (= (tptp.cons K L) tptp.nil))))
% 0.76/0.95 (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)))))))
% 0.76/0.95 (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)))))))
% 0.76/0.95 (assume a6 (= (tptp.length tptp.nil) 0))
% 0.76/0.95 (assume a7 (forall ((H Int) (T tptp.list)) (= (tptp.length (tptp.cons H T)) (+ 1 (tptp.length T)))))
% 0.76/0.95 (assume a8 (forall ((K Int)) (= (tptp.count K tptp.nil) 0)))
% 0.76/0.95 (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)))))
% 0.76/0.95 (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)))))
% 0.76/0.95 (assume a11 (forall ((L tptp.list)) (= (tptp.append tptp.nil L) L)))
% 0.76/0.95 (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)))))
% 0.76/0.95 (assume a13 (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0))))
% 0.76/0.95 (assume a14 (not (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))
% 0.76/0.95 (assume a15 true)
% 0.76/0.95 (step t1 (cl (not (= (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))))) (not (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule equiv_pos2)
% 0.76/0.95 (step t2 (cl (= (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule refl)
% 0.76/0.95 (step t3 (cl (= (= (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))))) :rule equiv_simplify)
% 0.76/0.95 (step t4 (cl (= (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (not (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))))) :rule equiv2 :premises (t3))
% 0.76/0.95 (step t5 (cl (not (not (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))))) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule not_not)
% 0.76/0.95 (step t6 (cl (= (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule resolution :premises (t4 t5))
% 0.76/0.95 (step t7 (cl (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule implies_neg1)
% 0.76/0.95 (anchor :step t8)
% 0.76/0.95 (assume t8.a0 (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))
% 0.76/0.95 (assume t8.a1 (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))
% 0.76/0.95 (step t8.t1 (cl (not (= (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule equiv_pos2)
% 0.76/0.95 (step t8.t2 (cl (= (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule all_simplify)
% 0.76/0.95 (step t8.t3 (cl (= (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule symm :premises (t8.t2))
% 0.76/0.95 (step t8.t4 (cl (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule implies_neg1)
% 0.76/0.95 (anchor :step t8.t5)
% 0.76/0.95 (assume t8.t5.a0 (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))
% 0.76/0.95 (step t8.t5.t1 (cl (not (= (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0))) false)) (not (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0)))) false) :rule equiv_pos2)
% 0.76/0.95 (step t8.t5.t2 (cl (= (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (to_real (* (- 1) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t3 (cl (= (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (to_real (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t4 (cl (= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (to_real (* (- 1) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (to_real (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule cong :premises (t8.t5.t2 t8.t5.t3))
% 0.76/0.95 (step t8.t5.t5 (cl (= (+ (to_real (* (- 1) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (to_real (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) 0.0)) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t6 (cl (= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) 0.0)) :rule trans :premises (t8.t5.t4 t8.t5.t5))
% 0.76/0.95 (step t8.t5.t7 (cl (= (* (- 1.0) 1) (- 1.0))) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t8 (cl (= (* 1.0 0) 0.0)) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t9 (cl (= (+ (* (- 1.0) 1) (* 1.0 0)) (+ (- 1.0) 0.0))) :rule cong :premises (t8.t5.t7 t8.t5.t8))
% 0.76/0.95 (step t8.t5.t10 (cl (= (+ (- 1.0) 0.0) (- 1.0))) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t11 (cl (= (+ (* (- 1.0) 1) (* 1.0 0)) (- 1.0))) :rule trans :premises (t8.t5.t9 t8.t5.t10))
% 0.76/0.95 (step t8.t5.t12 (cl (= (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0))) (<= 0.0 (- 1.0)))) :rule cong :premises (t8.t5.t6 t8.t5.t11))
% 0.76/0.95 (step t8.t5.t13 (cl (= (<= 0.0 (- 1.0)) false)) :rule all_simplify)
% 0.76/0.95 (step t8.t5.t14 (cl (= (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0))) false)) :rule trans :premises (t8.t5.t12 t8.t5.t13))
% 0.76/0.95 (step t8.t5.t15 (cl (not (<= (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* (- 1.0) 1))) (not (= (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 0))) (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0)))) :rule la_generic :args (1 (- 1) 1))
% 0.76/0.95 (step t8.t5.t16 (cl (=> (and (< (- 1.0) 0) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (<= (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* (- 1.0) 1)))) :rule la_mult_neg)
% 0.76/0.95 (step t8.t5.t17 (cl (not (and (< (- 1.0) 0) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (<= (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* (- 1.0) 1))) :rule implies :premises (t8.t5.t16))
% 0.76/0.95 (step t8.t5.t18 (cl (and (< (- 1.0) 0) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (not (< (- 1.0) 0)) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule and_neg)
% 0.76/0.95 (step t8.t5.t19 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.76/0.95 (step t8.t5.t20 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t8.t5.t19))
% 0.76/0.95 (step t8.t5.t21 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.76/0.95 (step t8.t5.t22 (cl (< (- 1.0) 0)) :rule resolution :premises (t8.t5.t20 t8.t5.t21))
% 0.76/0.95 (step t8.t5.t23 (cl (and (< (- 1.0) 0) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t8.t5.t18 t8.t5.t22 t8.t5.a0))
% 0.76/0.95 (step t8.t5.t24 (cl (<= (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* (- 1.0) 1))) :rule resolution :premises (t8.t5.t17 t8.t5.t23))
% 0.76/0.95 (step t8.t5.t25 (cl (=> (and (> 1.0 0) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0)) (= (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 0)))) :rule la_mult_pos)
% 0.76/0.95 (step t8.t5.t26 (cl (not (and (> 1.0 0) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0))) (= (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 0))) :rule implies :premises (t8.t5.t25))
% 0.76/0.95 (step t8.t5.t27 (cl (and (> 1.0 0) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0)) (not (> 1.0 0)) (not (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0))) :rule and_neg)
% 0.76/0.95 (step t8.t5.t28 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.76/0.95 (step t8.t5.t29 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t8.t5.t28))
% 0.76/0.95 (step t8.t5.t30 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.76/0.95 (step t8.t5.t31 (cl (> 1.0 0)) :rule resolution :premises (t8.t5.t29 t8.t5.t30))
% 0.76/0.95 (step t8.t5.t32 (cl (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0)) :rule symm :premises (t8.a1))
% 0.76/0.95 (step t8.t5.t33 (cl (and (> 1.0 0) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 0))) :rule resolution :premises (t8.t5.t27 t8.t5.t31 t8.t5.t32))
% 0.76/0.95 (step t8.t5.t34 (cl (= (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 0))) :rule resolution :premises (t8.t5.t26 t8.t5.t33))
% 0.76/0.95 (step t8.t5.t35 (cl (<= (+ (* (- 1.0) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (* 1.0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (+ (* (- 1.0) 1) (* 1.0 0)))) :rule resolution :premises (t8.t5.t15 t8.t5.t24 t8.t5.t34))
% 0.76/0.95 (step t8.t5.t36 (cl false) :rule resolution :premises (t8.t5.t1 t8.t5.t14 t8.t5.t35))
% 0.76/0.95 (step t8.t5 (cl (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) false) :rule subproof :discharge (t8.t5.a0))
% 0.76/0.95 (step t8.t6 (cl (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false) false) :rule resolution :premises (t8.t4 t8.t5))
% 0.76/0.95 (step t8.t7 (cl (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false) (not false)) :rule implies_neg2)
% 0.76/0.95 (step t8.t8 (cl (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false) (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false)) :rule resolution :premises (t8.t6 t8.t7))
% 0.76/0.95 (step t8.t9 (cl (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false)) :rule contraction :premises (t8.t8))
% 0.76/0.95 (step t8.t10 (cl (= (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule implies_simplify)
% 0.76/0.95 (step t8.t11 (cl (not (=> (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) false)) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule equiv1 :premises (t8.t10))
% 0.76/0.95 (step t8.t12 (cl (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t8.t9 t8.t11))
% 0.76/0.95 (step t8.t13 (cl (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule resolution :premises (t8.t1 t8.t3 t8.t12))
% 0.76/0.95 (step t8.t14 (cl (not (= (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule equiv_pos2)
% 0.76/0.95 (step t8.t15 (cl (= (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (not (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))))) :rule cong :premises (t8.t2))
% 0.76/0.95 (step t8.t16 (cl (= (not (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule all_simplify)
% 0.76/0.95 (step t8.t17 (cl (= (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule trans :premises (t8.t15 t8.t16))
% 0.76/0.95 (step t8.t18 (cl (= (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule symm :premises (t8.t17))
% 0.76/0.95 (step t8.t19 (cl (not (< (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t8.t14 t8.t18 t8.a0))
% 0.76/0.95 (step t8.t20 (cl) :rule resolution :premises (t8.t13 t8.t19))
% 0.76/0.95 (step t8 (cl (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (not (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) :rule subproof :discharge (t8.a0 t8.a1))
% 0.76/0.95 (step t9 (cl (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule and_pos)
% 0.76/0.95 (step t10 (cl (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule and_pos)
% 0.76/0.95 (step t11 (cl false (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule resolution :premises (t8 t9 t10))
% 0.76/0.95 (step t12 (cl (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) false) :rule reordering :premises (t11))
% 0.76/0.95 (step t13 (cl (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) false) :rule contraction :premises (t12))
% 0.76/0.95 (step t14 (cl (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) false) :rule resolution :premises (t7 t13))
% 0.76/0.95 (step t15 (cl (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (not false)) :rule implies_neg2)
% 0.76/0.95 (step t16 (cl (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false)) :rule resolution :premises (t14 t15))
% 0.76/0.95 (step t17 (cl (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false)) :rule contraction :premises (t16))
% 0.76/0.95 (step t18 (cl (= (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))))) :rule implies_simplify)
% 0.76/0.95 (step t19 (cl (not (=> (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false)) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule equiv1 :premises (t18))
% 0.76/0.95 (step t20 (cl (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule resolution :premises (t17 t19))
% 0.76/0.95 (step t21 (cl (= (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) false)) :rule resolution :premises (t6 t20))
% 0.76/0.95 (step t22 (cl (= (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) false))) :rule cong :premises (t2 t21))
% 0.76/0.95 (step t23 (cl (= (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) false) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))))) :rule all_simplify)
% 0.76/0.95 (step t24 (cl (= (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))))) :rule trans :premises (t22 t23))
% 0.76/0.95 (step t25 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule implies_neg1)
% 0.76/0.95 (anchor :step t26)
% 0.76/0.95 (assume t26.a0 (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))
% 0.76/0.95 (assume t26.a1 (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))
% 0.76/0.95 (assume t26.a2 (= (tptp.count 4 tptp.nil) 0))
% 0.76/0.95 (assume t26.a3 (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))
% 0.76/0.95 (assume t26.a4 (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))
% 0.76/0.95 (step t26.t1 (cl (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (not (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule and_neg)
% 0.76/0.95 (step t26.t2 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) :rule implies_neg1)
% 0.76/0.95 (anchor :step t26.t3)
% 0.76/0.95 (assume t26.t3.a0 (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))
% 0.76/0.95 (assume t26.t3.a1 (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))
% 0.76/0.95 (assume t26.t3.a2 (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))
% 0.76/0.95 (assume t26.t3.a3 (= (tptp.count 4 tptp.nil) 0))
% 0.76/0.95 (step t26.t3.t1 (cl (= 0 (tptp.count 4 tptp.nil))) :rule symm :premises (t26.t3.a3))
% 0.76/0.95 (step t26.t3.t2 (cl (= (tptp.count 4 tptp.nil) (tptp.count 4 (tptp.cons 3 tptp.nil)))) :rule symm :premises (t26.t3.a2))
% 0.76/0.95 (step t26.t3.t3 (cl (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))) :rule symm :premises (t26.t3.a1))
% 0.76/0.95 (step t26.t3.t4 (cl (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule symm :premises (t26.t3.t3))
% 0.76/0.95 (step t26.t3.t5 (cl (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule symm :premises (t26.t3.a0))
% 0.76/0.95 (step t26.t3.t6 (cl (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule trans :premises (t26.t3.t1 t26.t3.t2 t26.t3.t4 t26.t3.t5))
% 0.76/0.95 (step t26.t3 (cl (not (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (not (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule subproof :discharge (t26.t3.a0 t26.t3.a1 t26.t3.a2 t26.t3.a3))
% 0.76/0.95 (step t26.t4 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule and_pos)
% 0.76/0.95 (step t26.t5 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule and_pos)
% 0.76/0.95 (step t26.t6 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) :rule and_pos)
% 0.76/0.95 (step t26.t7 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= (tptp.count 4 tptp.nil) 0)) :rule and_pos)
% 0.76/0.95 (step t26.t8 (cl (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)))) :rule resolution :premises (t26.t3 t26.t4 t26.t5 t26.t6 t26.t7))
% 0.76/0.95 (step t26.t9 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule reordering :premises (t26.t8))
% 0.76/0.95 (step t26.t10 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule contraction :premises (t26.t9))
% 0.76/0.95 (step t26.t11 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t26.t2 t26.t10))
% 0.76/0.95 (step t26.t12 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (not (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule implies_neg2)
% 0.76/0.95 (step t26.t13 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule resolution :premises (t26.t11 t26.t12))
% 0.76/0.95 (step t26.t14 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule contraction :premises (t26.t13))
% 0.76/0.95 (step t26.t15 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule implies :premises (t26.t14))
% 0.76/0.95 (step t26.t16 (cl (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0)) (not (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (not (= (tptp.count 4 tptp.nil) 0))) :rule and_neg)
% 0.76/0.95 (step t26.t17 (cl (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0))) :rule resolution :premises (t26.t16 t26.a0 t26.a3 t26.a1 t26.a2))
% 0.76/0.95 (step t26.t18 (cl (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t26.t15 t26.t17))
% 0.76/0.95 (step t26.t19 (cl (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule resolution :premises (t26.t1 t26.a4 t26.t18))
% 0.76/0.95 (step t26 (cl (not (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (not (= (tptp.count 4 tptp.nil) 0)) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule subproof :discharge (t26.a0 t26.a1 t26.a2 t26.a3 t26.a4))
% 0.76/0.95 (step t27 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule and_pos)
% 0.76/0.95 (step t28 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) :rule and_pos)
% 0.76/0.95 (step t29 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (= (tptp.count 4 tptp.nil) 0)) :rule and_pos)
% 0.76/0.95 (step t30 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule and_pos)
% 0.76/0.95 (step t31 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule and_pos)
% 0.76/0.95 (step t32 (cl (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule resolution :premises (t26 t27 t28 t29 t30 t31))
% 0.76/0.95 (step t33 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule reordering :premises (t32))
% 0.76/0.95 (step t34 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule contraction :premises (t33))
% 0.76/0.95 (step t35 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule resolution :premises (t25 t34))
% 0.76/0.95 (step t36 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (not (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule implies_neg2)
% 0.76/0.95 (step t37 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule resolution :premises (t35 t36))
% 0.76/0.95 (step t38 (cl (=> (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) (and (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (= 0 (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))))) :rule contraction :premises (t37))
% 0.76/0.95 (step t39 (cl (not (and (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 tptp.nil) 0) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule resolution :premises (t1 t24 t38))
% 0.76/0.95 (step t40 (cl (not (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (not (= (tptp.count 4 tptp.nil) 0)) (not (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (not (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule not_and :premises (t39))
% 0.76/0.95 (step t41 (cl (not (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule equiv_pos2)
% 0.76/0.95 (step t42 (cl (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1) (not (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule reordering :premises (t41))
% 0.76/0.95 (step t43 (cl (not (= (not (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (not (not (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule equiv_pos2)
% 0.76/0.95 (step t44 (cl (= (not (not (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule all_simplify)
% 0.76/0.95 (step t45 (cl (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule resolution :premises (t43 t44 a14))
% 0.76/0.95 (step t46 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) :rule implies_neg1)
% 0.76/0.95 (anchor :step t47)
% 0.76/0.95 (assume t47.a0 (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))))
% 0.76/0.95 (step t47.t1 (cl (or (not (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule forall_inst :args ((:= N 4) (:= L (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))
% 0.76/0.95 (step t47.t2 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule or :premises (t47.t1))
% 0.76/0.95 (step t47.t3 (cl (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t47.t2 t47.a0))
% 0.76/0.95 (step t47 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule subproof :discharge (t47.a0))
% 0.76/0.95 (step t48 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t46 t47))
% 0.76/0.95 (step t49 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (not (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule implies_neg2)
% 0.76/0.95 (step t50 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule resolution :premises (t48 t49))
% 0.76/0.95 (step t51 (cl (=> (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)))) :rule contraction :premises (t50))
% 0.76/0.95 (step t52 (cl (not (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule implies :premises (t51))
% 0.76/0.95 (step t53 (cl (not (= (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0))) (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))))) (not (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0)))) (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) :rule equiv_pos2)
% 0.76/0.95 (anchor :step t54 :args ((N Int) (:= N N) (L tptp.list) (:= L L)))
% 0.76/0.95 (step t54.t1 (cl (= N N)) :rule refl)
% 0.76/0.95 (step t54.t2 (cl (= L L)) :rule refl)
% 0.76/0.95 (step t54.t3 (cl (= (tptp.in N L) (tptp.in N L))) :rule refl)
% 0.76/0.95 (step t54.t4 (cl (= (> (tptp.count N L) 0) (not (<= (tptp.count N L) 0)))) :rule all_simplify)
% 0.76/0.95 (step t54.t5 (cl (= (<= (tptp.count N L) 0) (not (>= (tptp.count N L) 1)))) :rule all_simplify)
% 0.76/0.95 (step t54.t6 (cl (= (not (<= (tptp.count N L) 0)) (not (not (>= (tptp.count N L) 1))))) :rule cong :premises (t54.t5))
% 0.76/0.95 (step t54.t7 (cl (= (not (not (>= (tptp.count N L) 1))) (>= (tptp.count N L) 1))) :rule all_simplify)
% 0.76/0.95 (step t54.t8 (cl (= (not (<= (tptp.count N L) 0)) (>= (tptp.count N L) 1))) :rule trans :premises (t54.t6 t54.t7))
% 0.76/0.95 (step t54.t9 (cl (= (> (tptp.count N L) 0) (>= (tptp.count N L) 1))) :rule trans :premises (t54.t4 t54.t8))
% 0.76/0.95 (step t54.t10 (cl (= (= (tptp.in N L) (> (tptp.count N L) 0)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) :rule cong :premises (t54.t3 t54.t9))
% 0.76/0.95 (step t54 (cl (= (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (> (tptp.count N L) 0))) (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1))))) :rule bind)
% 0.76/0.95 (step t55 (cl (forall ((N Int) (L tptp.list)) (= (tptp.in N L) (>= (tptp.count N L) 1)))) :rule resolution :premises (t53 t54 a13))
% 0.76/0.95 (step t56 (cl (= (tptp.in 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1))) :rule resolution :premises (t52 t55))
% 0.76/0.95 (step t57 (cl (>= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) 1)) :rule resolution :premises (t42 t45 t56))
% 0.76/0.95 (step t58 (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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule equiv_pos2)
% 0.76/0.95 (step t59 (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)
% 0.76/0.95 (step t60 (cl (= (= 4 2) false)) :rule all_simplify)
% 0.76/0.95 (step t61 (cl (= (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule all_simplify)
% 0.76/0.95 (step t62 (cl (= (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))) (or false (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule cong :premises (t60 t61))
% 0.76/0.95 (step t63 (cl (= (or false (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule all_simplify)
% 0.76/0.95 (step t64 (cl (= (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule trans :premises (t62 t63))
% 0.76/0.95 (step t65 (cl (= (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule cong :premises (t59 t64))
% 0.76/0.95 (step t66 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 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)
% 0.76/0.95 (anchor :step t67)
% 0.76/0.95 (assume t67.a0 (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))
% 0.76/0.95 (step t67.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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))))) :rule forall_inst :args ((:= K 4) (:= H 2) (:= T (tptp.cons 3 tptp.nil))))
% 0.76/0.95 (step t67.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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) :rule or :premises (t67.t1))
% 0.76/0.95 (step t67.t3 (cl (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) :rule resolution :premises (t67.t2 t67.a0))
% 0.76/0.95 (step t67 (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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) :rule subproof :discharge (t67.a0))
% 0.76/0.95 (step t68 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) :rule resolution :premises (t66 t67))
% 0.76/0.95 (step t69 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil))))) (not (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))))) :rule implies_neg2)
% 0.76/0.95 (step t70 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 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 (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t68 t69))
% 0.76/0.95 (step t71 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 2) (= (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))) (tptp.count 4 (tptp.cons 3 tptp.nil)))))) :rule contraction :premises (t70))
% 0.76/0.95 (step t72 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t58 t65 t71))
% 0.76/0.95 (step t73 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule implies :premises (t72))
% 0.76/0.95 (step t74 (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)
% 0.76/0.95 (step t75 (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)
% 0.76/0.95 (step t76 (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)
% 0.76/0.95 (step t77 (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 (t75 t76))
% 0.76/0.95 (step t78 (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 (t74 t77 a9))
% 0.76/0.95 (step t79 (cl (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule resolution :premises (t73 t78))
% 0.76/0.95 (step t80 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0)) (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) :rule implies_neg1)
% 0.76/0.95 (anchor :step t81)
% 0.76/0.95 (assume t81.a0 (forall ((K Int)) (= (tptp.count K tptp.nil) 0)))
% 0.76/0.95 (step t81.t1 (cl (or (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count 4 tptp.nil) 0))) :rule forall_inst :args ((:= K 4)))
% 0.76/0.95 (step t81.t2 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count 4 tptp.nil) 0)) :rule or :premises (t81.t1))
% 0.76/0.95 (step t81.t3 (cl (= (tptp.count 4 tptp.nil) 0)) :rule resolution :premises (t81.t2 t81.a0))
% 0.76/0.95 (step t81 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count 4 tptp.nil) 0)) :rule subproof :discharge (t81.a0))
% 0.76/0.95 (step t82 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0)) :rule resolution :premises (t80 t81))
% 0.76/0.95 (step t83 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0)) (not (= (tptp.count 4 tptp.nil) 0))) :rule implies_neg2)
% 0.76/0.95 (step t84 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0)) (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0))) :rule resolution :premises (t82 t83))
% 0.76/0.95 (step t85 (cl (=> (forall ((K Int)) (= (tptp.count K tptp.nil) 0)) (= (tptp.count 4 tptp.nil) 0))) :rule contraction :premises (t84))
% 0.76/0.95 (step t86 (cl (not (forall ((K Int)) (= (tptp.count K tptp.nil) 0))) (= (tptp.count 4 tptp.nil) 0)) :rule implies :premises (t85))
% 0.76/0.95 (step t87 (cl (= (tptp.count 4 tptp.nil) 0)) :rule resolution :premises (t86 a8))
% 0.76/0.95 (step t88 (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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule equiv_pos2)
% 0.76/0.95 (step t89 (cl (= (= 4 3) false)) :rule all_simplify)
% 0.76/0.95 (step t90 (cl (= (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule refl)
% 0.76/0.95 (step t91 (cl (= (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (or false (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule cong :premises (t89 t90))
% 0.76/0.95 (step t92 (cl (= (or false (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule all_simplify)
% 0.76/0.95 (step t93 (cl (= (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule trans :premises (t91 t92))
% 0.76/0.95 (step t94 (cl (= (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule cong :premises (t59 t93))
% 0.76/0.95 (step t95 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 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)
% 0.76/0.95 (anchor :step t96)
% 0.76/0.95 (assume t96.a0 (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))
% 0.76/0.95 (step t96.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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule forall_inst :args ((:= K 4) (:= H 3) (:= T tptp.nil)))
% 0.76/0.95 (step t96.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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule or :premises (t96.t1))
% 0.76/0.95 (step t96.t3 (cl (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule resolution :premises (t96.t2 t96.a0))
% 0.76/0.95 (step t96 (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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule subproof :discharge (t96.a0))
% 0.76/0.95 (step t97 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule resolution :premises (t95 t96))
% 0.76/0.95 (step t98 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) (not (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule implies_neg2)
% 0.76/0.95 (step t99 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 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 (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule resolution :premises (t97 t98))
% 0.76/0.95 (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)))) (or (= 4 3) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))))) :rule contraction :premises (t99))
% 0.76/0.95 (step t101 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil)))) :rule resolution :premises (t88 t94 t100))
% 0.76/0.95 (step t102 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) :rule implies :premises (t101))
% 0.76/0.95 (step t103 (cl (= (tptp.count 4 (tptp.cons 3 tptp.nil)) (tptp.count 4 tptp.nil))) :rule resolution :premises (t102 t78))
% 0.76/0.95 (step t104 (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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule equiv_pos2)
% 0.76/0.95 (step t105 (cl (= (= 4 1) false)) :rule all_simplify)
% 0.76/0.95 (step t106 (cl (= (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule refl)
% 0.76/0.95 (step t107 (cl (= (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (or false (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule cong :premises (t105 t106))
% 0.76/0.95 (step t108 (cl (= (or false (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule all_simplify)
% 0.76/0.95 (step t109 (cl (= (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule trans :premises (t107 t108))
% 0.76/0.95 (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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule cong :premises (t59 t109))
% 0.76/0.95 (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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 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)
% 0.78/0.95 (anchor :step t112)
% 0.78/0.95 (assume t112.a0 (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))))
% 0.78/0.95 (step t112.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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule forall_inst :args ((:= K 4) (:= H 1) (:= T (tptp.cons 2 (tptp.cons 3 tptp.nil)))))
% 0.78/0.95 (step t112.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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule or :premises (t112.t1))
% 0.78/0.95 (step t112.t3 (cl (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t112.t2 t112.a0))
% 0.78/0.95 (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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule subproof :discharge (t112.a0))
% 0.78/0.95 (step t113 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t111 t112))
% 0.78/0.95 (step t114 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) (not (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule implies_neg2)
% 0.78/0.95 (step t115 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 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 (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule resolution :premises (t113 t114))
% 0.78/0.95 (step t116 (cl (=> (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T)))) (or (= 4 1) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))))) :rule contraction :premises (t115))
% 0.78/0.95 (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)))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil)))))) :rule resolution :premises (t104 t110 t116))
% 0.78/0.95 (step t118 (cl (not (forall ((K Int) (H Int) (T tptp.list)) (or (= K H) (= (tptp.count K (tptp.cons H T)) (tptp.count K T))))) (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule implies :premises (t117))
% 0.78/0.95 (step t119 (cl (= (tptp.count 4 (tptp.cons 1 (tptp.cons 2 (tptp.cons 3 tptp.nil)))) (tptp.count 4 (tptp.cons 2 (tptp.cons 3 tptp.nil))))) :rule resolution :premises (t118 t78))
% 0.78/0.95 (step t120 (cl) :rule resolution :premises (t40 t57 t79 t87 t103 t119))
% 0.78/0.95
% 0.78/0.95 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.FQcW4yfAWz/cvc5---1.0.5_5189.smt2
% 0.78/0.95 % cvc5---1.0.5 exiting
% 0.78/0.95 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------