TSTP Solution File: SYN015-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN015-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 18:23:56 EDT 2024
% Result : Unsatisfiable 0.20s 0.57s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN015-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 28 13:39:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.Ach58sijBq/cvc5---1.0.5_27963.smt2
% 0.20/0.57 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.Ach58sijBq/cvc5---1.0.5_27963.smt2
% 0.55/0.71 (assume a0 (not (= tptp.m tptp.n)))
% 0.55/0.71 (assume a1 (forall ((Y $$unsorted)) (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j))))
% 0.55/0.71 (assume a2 (forall ((Y $$unsorted)) (or (= Y tptp.j) (= Y tptp.k) (not (tptp.element Y tptp.j)))))
% 0.55/0.71 (assume a3 (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) tptp.m)))))
% 0.55/0.71 (assume a4 (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) Y)))))
% 0.55/0.71 (assume a5 (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))
% 0.55/0.71 (assume a6 (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))
% 0.55/0.71 (assume a7 (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= Y tptp.m) (tptp.element Y tptp.m) (= V1 tptp.m) (= V1 Y) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))
% 0.55/0.71 (assume a8 (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) tptp.n)))))
% 0.55/0.71 (assume a9 (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) Y)))))
% 0.55/0.71 (assume a10 (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))))
% 0.55/0.71 (assume a11 (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))))
% 0.55/0.71 (assume a12 (forall ((Y $$unsorted) (V $$unsorted)) (or (= Y tptp.n) (not (tptp.element Y tptp.n)) (= V tptp.n) (= V Y) (not (tptp.element Y V)) (not (tptp.element V Y)))))
% 0.55/0.71 (assume a13 (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k))))
% 0.55/0.71 (assume a14 (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k))))
% 0.55/0.71 (assume a15 (forall ((Y $$unsorted)) (or (= Y tptp.k) (= Y tptp.m) (= Y tptp.n) (not (tptp.element Y tptp.k)))))
% 0.55/0.71 (step t1 (cl (not (= (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.n tptp.k)) (= tptp.j tptp.k) (not (= tptp.n tptp.j))))) (not (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j)))) (or (not (= tptp.n tptp.k)) (= tptp.j tptp.k) (not (= tptp.n tptp.j)))) :rule equiv_pos2)
% 0.55/0.71 (step t2 (cl (= (not (= tptp.n tptp.k)) (not (= tptp.n tptp.k)))) :rule refl)
% 0.55/0.71 (step t3 (cl (= (= (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k)) true) (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k)))) :rule equiv_simplify)
% 0.55/0.71 (step t4 (cl (not (= (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k)) true)) (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k))) :rule equiv1 :premises (t3))
% 0.55/0.71 (step t5 (cl (= (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k)) (= (= tptp.j tptp.k) (not (not (= tptp.j tptp.k)))))) :rule all_simplify)
% 0.55/0.71 (step t6 (cl (= (= tptp.j tptp.k) (= tptp.j tptp.k))) :rule refl)
% 0.55/0.71 (step t7 (cl (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k))) :rule all_simplify)
% 0.55/0.71 (step t8 (cl (= (= (= tptp.j tptp.k) (not (not (= tptp.j tptp.k)))) (= (= tptp.j tptp.k) (= tptp.j tptp.k)))) :rule cong :premises (t6 t7))
% 0.55/0.71 (step t9 (cl (= (= (= tptp.j tptp.k) (= tptp.j tptp.k)) true)) :rule all_simplify)
% 0.55/0.71 (step t10 (cl (= (= (= tptp.j tptp.k) (not (not (= tptp.j tptp.k)))) true)) :rule trans :premises (t8 t9))
% 0.55/0.71 (step t11 (cl (= (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k)) true)) :rule trans :premises (t5 t10))
% 0.55/0.71 (step t12 (cl (= (not (not (= tptp.j tptp.k))) (= tptp.j tptp.k))) :rule resolution :premises (t4 t11))
% 0.55/0.71 (step t13 (cl (= (not (= tptp.n tptp.j)) (not (= tptp.n tptp.j)))) :rule refl)
% 0.55/0.71 (step t14 (cl (= (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.n tptp.k)) (= tptp.j tptp.k) (not (= tptp.n tptp.j))))) :rule cong :premises (t2 t12 t13))
% 0.55/0.71 (step t15 (cl (not (= (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))))) (not (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)))) :rule equiv_pos2)
% 0.55/0.71 (step t16 (cl (= (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)))) :rule refl)
% 0.55/0.71 (step t17 (cl (= (= (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))))) :rule equiv_simplify)
% 0.55/0.71 (step t18 (cl (= (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (not (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))))) :rule equiv2 :premises (t17))
% 0.55/0.71 (step t19 (cl (not (not (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))))) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule not_not)
% 0.55/0.71 (step t20 (cl (= (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule resolution :premises (t18 t19))
% 0.55/0.71 (step t21 (cl (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule implies_neg1)
% 0.55/0.71 (anchor :step t22)
% 0.55/0.71 (assume t22.a0 (= tptp.n tptp.k))
% 0.55/0.71 (assume t22.a1 (= tptp.n tptp.j))
% 0.55/0.71 (assume t22.a2 (not (= tptp.j tptp.k)))
% 0.55/0.71 (step t22.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 0.55/0.71 (step t22.t2 (cl (= (= false true) false)) :rule all_simplify)
% 0.55/0.71 (step t22.t3 (cl (= (= (= tptp.j tptp.k) false) (not (= tptp.j tptp.k)))) :rule equiv_simplify)
% 0.55/0.71 (step t22.t4 (cl (= (= tptp.j tptp.k) false) (not (not (= tptp.j tptp.k)))) :rule equiv2 :premises (t22.t3))
% 0.55/0.71 (step t22.t5 (cl (not (not (not (= tptp.j tptp.k)))) (= tptp.j tptp.k)) :rule not_not)
% 0.55/0.71 (step t22.t6 (cl (= (= tptp.j tptp.k) false) (= tptp.j tptp.k)) :rule resolution :premises (t22.t4 t22.t5))
% 0.55/0.71 (step t22.t7 (cl (= (= tptp.j tptp.k) false)) :rule resolution :premises (t22.t6 t22.a2))
% 0.55/0.71 (step t22.t8 (cl (= false (= tptp.j tptp.k))) :rule symm :premises (t22.t7))
% 0.55/0.71 (step t22.t9 (cl (= (= (= tptp.j tptp.k) true) (= tptp.j tptp.k))) :rule equiv_simplify)
% 0.55/0.71 (step t22.t10 (cl (= (= tptp.j tptp.k) true) (not (= tptp.j tptp.k))) :rule equiv2 :premises (t22.t9))
% 0.55/0.71 (step t22.t11 (cl (= tptp.j tptp.n)) :rule symm :premises (t22.a1))
% 0.55/0.71 (step t22.t12 (cl (= tptp.k tptp.n)) :rule symm :premises (t22.a0))
% 0.55/0.71 (step t22.t13 (cl (= tptp.n tptp.k)) :rule symm :premises (t22.t12))
% 0.55/0.71 (step t22.t14 (cl (= tptp.j tptp.k)) :rule trans :premises (t22.t11 t22.t13))
% 0.55/0.71 (step t22.t15 (cl (= (= tptp.j tptp.k) true)) :rule resolution :premises (t22.t10 t22.t14))
% 0.55/0.71 (step t22.t16 (cl (= false true)) :rule trans :premises (t22.t8 t22.t15))
% 0.55/0.71 (step t22.t17 (cl false) :rule resolution :premises (t22.t1 t22.t2 t22.t16))
% 0.55/0.71 (step t22 (cl (not (= tptp.n tptp.k)) (not (= tptp.n tptp.j)) (not (not (= tptp.j tptp.k))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.55/0.71 (step t23 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.71 (step t24 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (= tptp.n tptp.j)) :rule and_pos)
% 0.55/0.71 (step t25 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (= tptp.j tptp.k))) :rule and_pos)
% 0.55/0.71 (step t26 (cl false (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule resolution :premises (t22 t23 t24 t25))
% 0.55/0.71 (step t27 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) false) :rule reordering :premises (t26))
% 0.55/0.71 (step t28 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) false) :rule contraction :premises (t27))
% 0.55/0.71 (step t29 (cl (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) false) :rule resolution :premises (t21 t28))
% 0.55/0.71 (step t30 (cl (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (not false)) :rule implies_neg2)
% 0.55/0.71 (step t31 (cl (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false)) :rule resolution :premises (t29 t30))
% 0.55/0.71 (step t32 (cl (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false)) :rule contraction :premises (t31))
% 0.55/0.71 (step t33 (cl (= (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))))) :rule implies_simplify)
% 0.55/0.71 (step t34 (cl (not (=> (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false)) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule equiv1 :premises (t33))
% 0.55/0.71 (step t35 (cl (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule resolution :premises (t32 t34))
% 0.55/0.71 (step t36 (cl (= (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) false)) :rule resolution :premises (t20 t35))
% 0.55/0.71 (step t37 (cl (= (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) false))) :rule cong :premises (t16 t36))
% 0.55/0.71 (step t38 (cl (= (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) false) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))))) :rule all_simplify)
% 0.55/0.71 (step t39 (cl (= (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))))) :rule trans :premises (t37 t38))
% 0.55/0.71 (step t40 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) :rule implies_neg1)
% 0.55/0.71 (anchor :step t41)
% 0.55/0.71 (assume t41.a0 (= tptp.n tptp.k))
% 0.55/0.71 (assume t41.a1 (not (= tptp.j tptp.k)))
% 0.55/0.71 (assume t41.a2 (= tptp.n tptp.j))
% 0.55/0.71 (step t41.t1 (cl (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) (not (= tptp.n tptp.k)) (not (= tptp.n tptp.j)) (not (not (= tptp.j tptp.k)))) :rule and_neg)
% 0.55/0.71 (step t41.t2 (cl (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule resolution :premises (t41.t1 t41.a0 t41.a2 t41.a1))
% 0.55/0.71 (step t41 (cl (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.55/0.71 (step t42 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.71 (step t43 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (not (= tptp.j tptp.k))) :rule and_pos)
% 0.55/0.71 (step t44 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (= tptp.n tptp.j)) :rule and_pos)
% 0.55/0.71 (step t45 (cl (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)))) :rule resolution :premises (t41 t42 t43 t44))
% 0.55/0.72 (step t46 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule reordering :premises (t45))
% 0.55/0.72 (step t47 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j))) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule contraction :premises (t46))
% 0.55/0.72 (step t48 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) :rule resolution :premises (t40 t47))
% 0.55/0.72 (step t49 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t50 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k)))) (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule resolution :premises (t48 t49))
% 0.55/0.72 (step t51 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)) (and (= tptp.n tptp.k) (= tptp.n tptp.j) (not (= tptp.j tptp.k))))) :rule contraction :premises (t50))
% 0.55/0.72 (step t52 (cl (not (and (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.j)))) :rule resolution :premises (t15 t39 t51))
% 0.55/0.72 (step t53 (cl (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) :rule not_and :premises (t52))
% 0.55/0.72 (step t54 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t55 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (not (not (not (= tptp.j tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t56 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (not (not (= tptp.n tptp.j)))) :rule or_neg)
% 0.55/0.72 (step t57 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j)))) :rule resolution :premises (t53 t54 t55 t56))
% 0.55/0.72 (step t58 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.j tptp.k))) (not (= tptp.n tptp.j)))) :rule contraction :premises (t57))
% 0.55/0.72 (step t59 (cl (or (not (= tptp.n tptp.k)) (= tptp.j tptp.k) (not (= tptp.n tptp.j)))) :rule resolution :premises (t1 t14 t58))
% 0.55/0.72 (step t60 (cl (not (= tptp.n tptp.k)) (= tptp.j tptp.k) (not (= tptp.n tptp.j))) :rule or :premises (t59))
% 0.55/0.72 (step t61 (cl (= tptp.j tptp.k) (not (= tptp.n tptp.k)) (not (= tptp.n tptp.j))) :rule reordering :premises (t60))
% 0.55/0.72 (step t62 (cl (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (not (= tptp.n tptp.k)) (not (= tptp.k (tptp.g tptp.j)))) :rule and_neg)
% 0.55/0.72 (step t63 (cl (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t64)
% 0.55/0.72 (assume t64.a0 (= tptp.n tptp.k))
% 0.55/0.72 (assume t64.a1 (= tptp.k (tptp.g tptp.j)))
% 0.55/0.72 (step t64.t1 (cl (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j))) (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t64.t2)
% 0.55/0.72 (assume t64.t2.a0 (= tptp.k (tptp.g tptp.j)))
% 0.55/0.72 (assume t64.t2.a1 (= tptp.n tptp.k))
% 0.55/0.72 (step t64.t2.t1 (cl (= tptp.k tptp.n)) :rule symm :premises (t64.t2.a1))
% 0.55/0.72 (step t64.t2.t2 (cl (= tptp.n tptp.k)) :rule symm :premises (t64.t2.t1))
% 0.55/0.72 (step t64.t2.t3 (cl (= (tptp.g tptp.j) tptp.k)) :rule symm :premises (t64.t2.a0))
% 0.55/0.72 (step t64.t2.t4 (cl (= tptp.k (tptp.g tptp.j))) :rule symm :premises (t64.t2.t3))
% 0.55/0.72 (step t64.t2.t5 (cl (= tptp.n (tptp.g tptp.j))) :rule trans :premises (t64.t2.t2 t64.t2.t4))
% 0.55/0.72 (step t64.t2 (cl (not (= tptp.k (tptp.g tptp.j))) (not (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j))) :rule subproof :discharge (t64.t2.a0 t64.t2.a1))
% 0.55/0.72 (step t64.t3 (cl (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (= tptp.k (tptp.g tptp.j))) :rule and_pos)
% 0.55/0.72 (step t64.t4 (cl (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t64.t5 (cl (= tptp.n (tptp.g tptp.j)) (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)))) :rule resolution :premises (t64.t2 t64.t3 t64.t4))
% 0.55/0.72 (step t64.t6 (cl (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (= tptp.n (tptp.g tptp.j))) :rule reordering :premises (t64.t5))
% 0.55/0.72 (step t64.t7 (cl (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (= tptp.n (tptp.g tptp.j))) :rule contraction :premises (t64.t6))
% 0.55/0.72 (step t64.t8 (cl (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) :rule resolution :premises (t64.t1 t64.t7))
% 0.55/0.72 (step t64.t9 (cl (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j))) (not (= tptp.n (tptp.g tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t64.t10 (cl (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j))) (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j)))) :rule resolution :premises (t64.t8 t64.t9))
% 0.55/0.72 (step t64.t11 (cl (=> (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j)))) :rule contraction :premises (t64.t10))
% 0.55/0.72 (step t64.t12 (cl (not (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) (= tptp.n (tptp.g tptp.j))) :rule implies :premises (t64.t11))
% 0.55/0.72 (step t64.t13 (cl (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k)) (not (= tptp.k (tptp.g tptp.j))) (not (= tptp.n tptp.k))) :rule and_neg)
% 0.55/0.72 (step t64.t14 (cl (and (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.k))) :rule resolution :premises (t64.t13 t64.a1 t64.a0))
% 0.55/0.72 (step t64.t15 (cl (= tptp.n (tptp.g tptp.j))) :rule resolution :premises (t64.t12 t64.t14))
% 0.55/0.72 (step t64 (cl (not (= tptp.n tptp.k)) (not (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) :rule subproof :discharge (t64.a0 t64.a1))
% 0.55/0.72 (step t65 (cl (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t66 (cl (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (= tptp.k (tptp.g tptp.j))) :rule and_pos)
% 0.55/0.72 (step t67 (cl (= tptp.n (tptp.g tptp.j)) (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))))) :rule resolution :premises (t64 t65 t66))
% 0.55/0.72 (step t68 (cl (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (= tptp.n (tptp.g tptp.j))) :rule reordering :premises (t67))
% 0.55/0.72 (step t69 (cl (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (= tptp.n (tptp.g tptp.j))) :rule contraction :premises (t68))
% 0.55/0.72 (step t70 (cl (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) :rule resolution :premises (t63 t69))
% 0.55/0.72 (step t71 (cl (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) (not (= tptp.n (tptp.g tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t72 (cl (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j)))) :rule resolution :premises (t70 t71))
% 0.55/0.72 (step t73 (cl (=> (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j)))) :rule contraction :premises (t72))
% 0.55/0.72 (step t74 (cl (not (and (= tptp.n tptp.k) (= tptp.k (tptp.g tptp.j)))) (= tptp.n (tptp.g tptp.j))) :rule implies :premises (t73))
% 0.55/0.72 (step t75 (cl (not (= tptp.n tptp.k)) (not (= tptp.k (tptp.g tptp.j))) (= tptp.n (tptp.g tptp.j))) :rule resolution :premises (t62 t74))
% 0.55/0.72 (step t76 (cl (not (= tptp.n tptp.k)) (= tptp.n (tptp.g tptp.j)) (not (= tptp.k (tptp.g tptp.j)))) :rule reordering :premises (t75))
% 0.55/0.72 (step t77 (cl (not (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))) :rule or_pos)
% 0.55/0.72 (step t78 (cl (= tptp.n tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.k tptp.n)) (not (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule reordering :premises (t77))
% 0.55/0.72 (step t79 (cl (not (= (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))))) (not (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t80 (cl (= (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))))) :rule refl)
% 0.55/0.72 (step t81 (cl (= (= tptp.n tptp.k) (= tptp.n tptp.k))) :rule refl)
% 0.55/0.72 (step t82 (cl (= (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.k tptp.n)))) :rule refl)
% 0.55/0.72 (step t83 (cl (= (= tptp.n tptp.m) (= tptp.n tptp.m))) :rule refl)
% 0.55/0.72 (step t84 (cl (= (= tptp.k tptp.m) (= tptp.m tptp.k))) :rule all_simplify)
% 0.55/0.72 (step t85 (cl (= (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.k tptp.m)))) :rule refl)
% 0.55/0.72 (step t86 (cl (= (not (tptp.element tptp.m tptp.k)) (not (tptp.element tptp.m tptp.k)))) :rule refl)
% 0.55/0.72 (step t87 (cl (= (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule cong :premises (t81 t82 t83 t84 t85 t86))
% 0.55/0.72 (step t88 (cl (= (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))))) :rule cong :premises (t80 t87))
% 0.55/0.72 (step t89 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t90)
% 0.55/0.72 (assume t90.a0 (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))))
% 0.55/0.72 (step t90.t1 (cl (or (not (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule forall_inst :args ((:= Y tptp.k) (:= V tptp.m)))
% 0.55/0.72 (step t90.t2 (cl (not (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule or :premises (t90.t1))
% 0.55/0.72 (step t90.t3 (cl (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t90.t2 t90.a0))
% 0.55/0.72 (step t90 (cl (not (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule subproof :discharge (t90.a0))
% 0.55/0.72 (step t91 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t89 t90))
% 0.55/0.72 (step t92 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (not (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t93 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule resolution :premises (t91 t92))
% 0.55/0.72 (step t94 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule contraction :premises (t93))
% 0.55/0.72 (step t95 (cl (=> (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k))))) :rule resolution :premises (t79 t88 t94))
% 0.55/0.72 (step t96 (cl (not (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule implies :premises (t95))
% 0.55/0.72 (step t97 (cl (not (= (forall ((Y $$unsorted) (V $$unsorted)) (or (= Y tptp.n) (not (tptp.element Y tptp.n)) (= V tptp.n) (= V Y) (not (tptp.element Y V)) (not (tptp.element V Y)))) (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))))) (not (forall ((Y $$unsorted) (V $$unsorted)) (or (= Y tptp.n) (not (tptp.element Y tptp.n)) (= V tptp.n) (= V Y) (not (tptp.element Y V)) (not (tptp.element V Y))))) (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t98 :args ((Y $$unsorted) (:= Y Y) (V $$unsorted) (:= V V)))
% 0.55/0.72 (step t98.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t98.t2 (cl (= V V)) :rule refl)
% 0.55/0.72 (step t98.t3 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t98.t4 (cl (= (not (tptp.element Y tptp.n)) (not (tptp.element Y tptp.n)))) :rule refl)
% 0.55/0.72 (step t98.t5 (cl (= (= V tptp.n) (= tptp.n V))) :rule all_simplify)
% 0.55/0.72 (step t98.t6 (cl (= (= V Y) (= Y V))) :rule all_simplify)
% 0.55/0.72 (step t98.t7 (cl (= (not (tptp.element Y V)) (not (tptp.element Y V)))) :rule refl)
% 0.55/0.72 (step t98.t8 (cl (= (not (tptp.element V Y)) (not (tptp.element V Y)))) :rule refl)
% 0.55/0.72 (step t98.t9 (cl (= (or (= Y tptp.n) (not (tptp.element Y tptp.n)) (= V tptp.n) (= V Y) (not (tptp.element Y V)) (not (tptp.element V Y))) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) :rule cong :premises (t98.t3 t98.t4 t98.t5 t98.t6 t98.t7 t98.t8))
% 0.55/0.72 (step t98 (cl (= (forall ((Y $$unsorted) (V $$unsorted)) (or (= Y tptp.n) (not (tptp.element Y tptp.n)) (= V tptp.n) (= V Y) (not (tptp.element Y V)) (not (tptp.element V Y)))) (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y)))))) :rule bind)
% 0.55/0.72 (step t99 (cl (forall ((Y $$unsorted) (V $$unsorted)) (or (= tptp.n Y) (not (tptp.element Y tptp.n)) (= tptp.n V) (= Y V) (not (tptp.element Y V)) (not (tptp.element V Y))))) :rule resolution :premises (t97 t98 a12))
% 0.55/0.72 (step t100 (cl (or (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (= tptp.n tptp.m) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t96 t99))
% 0.55/0.72 (step t101 (cl (not (= tptp.n tptp.m))) :rule not_symm :premises (a0))
% 0.55/0.72 (step t102 (cl (not (= (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (or (tptp.element tptp.k tptp.n) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))))) (not (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) (or (tptp.element tptp.k tptp.n) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t103 (cl (= (= (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n)) true) (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n)))) :rule equiv_simplify)
% 0.55/0.72 (step t104 (cl (not (= (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n)) true)) (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n))) :rule equiv1 :premises (t103))
% 0.55/0.72 (step t105 (cl (= (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n)) (= (tptp.element tptp.k tptp.n) (not (not (tptp.element tptp.k tptp.n)))))) :rule all_simplify)
% 0.55/0.72 (step t106 (cl (= (tptp.element tptp.k tptp.n) (tptp.element tptp.k tptp.n))) :rule refl)
% 0.55/0.72 (step t107 (cl (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n))) :rule all_simplify)
% 0.55/0.72 (step t108 (cl (= (= (tptp.element tptp.k tptp.n) (not (not (tptp.element tptp.k tptp.n)))) (= (tptp.element tptp.k tptp.n) (tptp.element tptp.k tptp.n)))) :rule cong :premises (t106 t107))
% 0.55/0.72 (step t109 (cl (= (= (tptp.element tptp.k tptp.n) (tptp.element tptp.k tptp.n)) true)) :rule all_simplify)
% 0.55/0.72 (step t110 (cl (= (= (tptp.element tptp.k tptp.n) (not (not (tptp.element tptp.k tptp.n)))) true)) :rule trans :premises (t108 t109))
% 0.55/0.72 (step t111 (cl (= (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n)) true)) :rule trans :premises (t105 t110))
% 0.55/0.72 (step t112 (cl (= (not (not (tptp.element tptp.k tptp.n))) (tptp.element tptp.k tptp.n))) :rule resolution :premises (t104 t111))
% 0.55/0.72 (step t113 (cl (= (not (tptp.element tptp.k (tptp.f tptp.k))) (not (tptp.element tptp.k (tptp.f tptp.k))))) :rule refl)
% 0.55/0.72 (step t114 (cl (= (not (= tptp.n (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) :rule refl)
% 0.55/0.72 (step t115 (cl (= (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (or (tptp.element tptp.k tptp.n) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))))) :rule cong :premises (t112 t113 t114))
% 0.55/0.72 (step t116 (cl (not (= (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))))) (not (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t117 (cl (= (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))))) :rule refl)
% 0.55/0.72 (step t118 (cl (= (= (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))))) :rule equiv_simplify)
% 0.55/0.72 (step t119 (cl (= (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (not (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))))) :rule equiv2 :premises (t118))
% 0.55/0.72 (step t120 (cl (not (not (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule not_not)
% 0.55/0.72 (step t121 (cl (= (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t119 t120))
% 0.55/0.72 (step t122 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t123)
% 0.55/0.72 (assume t123.a0 (not (tptp.element tptp.k tptp.n)))
% 0.55/0.72 (assume t123.a1 (= tptp.n (tptp.f tptp.k)))
% 0.55/0.72 (assume t123.a2 (tptp.element tptp.k (tptp.f tptp.k)))
% 0.55/0.72 (step t123.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.55/0.72 (step t123.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.55/0.72 (step t123.t3 (cl (= (= (tptp.element tptp.k (tptp.f tptp.k)) true) (tptp.element tptp.k (tptp.f tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t123.t4 (cl (= (tptp.element tptp.k (tptp.f tptp.k)) true) (not (tptp.element tptp.k (tptp.f tptp.k)))) :rule equiv2 :premises (t123.t3))
% 0.55/0.72 (step t123.t5 (cl (= (tptp.element tptp.k (tptp.f tptp.k)) true)) :rule resolution :premises (t123.t4 t123.a2))
% 0.55/0.72 (step t123.t6 (cl (= true (tptp.element tptp.k (tptp.f tptp.k)))) :rule symm :premises (t123.t5))
% 0.55/0.72 (step t123.t7 (cl (= tptp.k tptp.k)) :rule refl)
% 0.55/0.72 (step t123.t8 (cl (= (tptp.f tptp.k) tptp.n)) :rule symm :premises (t123.a1))
% 0.55/0.72 (step t123.t9 (cl (= (tptp.element tptp.k (tptp.f tptp.k)) (tptp.element tptp.k tptp.n))) :rule cong :premises (t123.t7 t123.t8))
% 0.55/0.72 (step t123.t10 (cl (= (= (tptp.element tptp.k tptp.n) false) (not (tptp.element tptp.k tptp.n)))) :rule equiv_simplify)
% 0.55/0.72 (step t123.t11 (cl (= (tptp.element tptp.k tptp.n) false) (not (not (tptp.element tptp.k tptp.n)))) :rule equiv2 :premises (t123.t10))
% 0.55/0.72 (step t123.t12 (cl (not (not (not (tptp.element tptp.k tptp.n)))) (tptp.element tptp.k tptp.n)) :rule not_not)
% 0.55/0.72 (step t123.t13 (cl (= (tptp.element tptp.k tptp.n) false) (tptp.element tptp.k tptp.n)) :rule resolution :premises (t123.t11 t123.t12))
% 0.55/0.72 (step t123.t14 (cl (= (tptp.element tptp.k tptp.n) false)) :rule resolution :premises (t123.t13 t123.a0))
% 0.55/0.72 (step t123.t15 (cl (= true false)) :rule trans :premises (t123.t6 t123.t9 t123.t14))
% 0.55/0.72 (step t123.t16 (cl false) :rule resolution :premises (t123.t1 t123.t2 t123.t15))
% 0.55/0.72 (step t123 (cl (not (not (tptp.element tptp.k tptp.n))) (not (= tptp.n (tptp.f tptp.k))) (not (tptp.element tptp.k (tptp.f tptp.k))) false) :rule subproof :discharge (t123.a0 t123.a1 t123.a2))
% 0.55/0.72 (step t124 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (tptp.element tptp.k tptp.n))) :rule and_pos)
% 0.55/0.72 (step t125 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (= tptp.n (tptp.f tptp.k))) :rule and_pos)
% 0.55/0.72 (step t126 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (tptp.element tptp.k (tptp.f tptp.k))) :rule and_pos)
% 0.55/0.72 (step t127 (cl false (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t123 t124 t125 t126))
% 0.55/0.72 (step t128 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) false) :rule reordering :premises (t127))
% 0.55/0.72 (step t129 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) false) :rule contraction :premises (t128))
% 0.55/0.72 (step t130 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) false) :rule resolution :premises (t122 t129))
% 0.55/0.72 (step t131 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t132 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false)) :rule resolution :premises (t130 t131))
% 0.55/0.72 (step t133 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false)) :rule contraction :premises (t132))
% 0.55/0.72 (step t134 (cl (= (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))))) :rule implies_simplify)
% 0.55/0.72 (step t135 (cl (not (=> (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false)) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule equiv1 :premises (t134))
% 0.55/0.72 (step t136 (cl (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t133 t135))
% 0.55/0.72 (step t137 (cl (= (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) false)) :rule resolution :premises (t121 t136))
% 0.55/0.72 (step t138 (cl (= (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) false))) :rule cong :premises (t117 t137))
% 0.55/0.72 (step t139 (cl (= (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))))) :rule all_simplify)
% 0.55/0.72 (step t140 (cl (= (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))))) :rule trans :premises (t138 t139))
% 0.55/0.72 (step t141 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t142)
% 0.55/0.72 (assume t142.a0 (not (tptp.element tptp.k tptp.n)))
% 0.55/0.72 (assume t142.a1 (tptp.element tptp.k (tptp.f tptp.k)))
% 0.55/0.72 (assume t142.a2 (= tptp.n (tptp.f tptp.k)))
% 0.55/0.72 (step t142.t1 (cl (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) (not (not (tptp.element tptp.k tptp.n))) (not (= tptp.n (tptp.f tptp.k))) (not (tptp.element tptp.k (tptp.f tptp.k)))) :rule and_neg)
% 0.55/0.72 (step t142.t2 (cl (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t142.t1 t142.a0 t142.a2 t142.a1))
% 0.55/0.72 (step t142 (cl (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule subproof :discharge (t142.a0 t142.a1 t142.a2))
% 0.55/0.72 (step t143 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (not (tptp.element tptp.k tptp.n))) :rule and_pos)
% 0.55/0.72 (step t144 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (tptp.element tptp.k (tptp.f tptp.k))) :rule and_pos)
% 0.55/0.72 (step t145 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (= tptp.n (tptp.f tptp.k))) :rule and_pos)
% 0.55/0.72 (step t146 (cl (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t142 t143 t144 t145))
% 0.55/0.72 (step t147 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule reordering :premises (t146))
% 0.55/0.72 (step t148 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule contraction :premises (t147))
% 0.55/0.72 (step t149 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t141 t148))
% 0.55/0.72 (step t150 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t151 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k)))) (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t149 t150))
% 0.55/0.72 (step t152 (cl (=> (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))) (and (not (tptp.element tptp.k tptp.n)) (= tptp.n (tptp.f tptp.k)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule contraction :premises (t151))
% 0.55/0.72 (step t153 (cl (not (and (not (tptp.element tptp.k tptp.n)) (tptp.element tptp.k (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t116 t140 t152))
% 0.55/0.72 (step t154 (cl (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) :rule not_and :premises (t153))
% 0.55/0.72 (step t155 (cl (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (not (tptp.element tptp.k tptp.n))))) :rule or_neg)
% 0.55/0.72 (step t156 (cl (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (tptp.element tptp.k (tptp.f tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t157 (cl (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (= tptp.n (tptp.f tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t158 (cl (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t154 t155 t156 t157))
% 0.55/0.72 (step t159 (cl (or (not (not (tptp.element tptp.k tptp.n))) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) :rule contraction :premises (t158))
% 0.55/0.72 (step t160 (cl (or (tptp.element tptp.k tptp.n) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t102 t115 t159))
% 0.55/0.72 (step t161 (cl (tptp.element tptp.k tptp.n) (not (tptp.element tptp.k (tptp.f tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) :rule or :premises (t160))
% 0.55/0.72 (step t162 (cl (not (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))) :rule or_pos)
% 0.55/0.72 (step t163 (cl (= tptp.m (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))))) :rule reordering :premises (t162))
% 0.55/0.72 (step t164 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t165)
% 0.55/0.72 (assume t165.a0 (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))))
% 0.55/0.72 (step t165.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))))) :rule forall_inst :args ((:= Y (tptp.f tptp.k))))
% 0.55/0.72 (step t165.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule or :premises (t165.t1))
% 0.55/0.72 (step t165.t3 (cl (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule resolution :premises (t165.t2 t165.a0))
% 0.55/0.72 (step t165 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule subproof :discharge (t165.a0))
% 0.55/0.72 (step t166 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule resolution :premises (t164 t165))
% 0.55/0.72 (step t167 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) (not (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t168 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))))) :rule resolution :premises (t166 t167))
% 0.55/0.72 (step t169 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k))))) :rule contraction :premises (t168))
% 0.55/0.72 (step t170 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule implies :premises (t169))
% 0.55/0.72 (step t171 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (= Y tptp.m) (= Y tptp.n) (not (tptp.element Y tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.k) (= Y tptp.m) (= Y tptp.n) (not (tptp.element Y tptp.k))))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t172 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t172.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t172.t2 (cl (= (= Y tptp.k) (= tptp.k Y))) :rule all_simplify)
% 0.55/0.72 (step t172.t3 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t172.t4 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t172.t5 (cl (= (not (tptp.element Y tptp.k)) (not (tptp.element Y tptp.k)))) :rule refl)
% 0.55/0.72 (step t172.t6 (cl (= (or (= Y tptp.k) (= Y tptp.m) (= Y tptp.n) (not (tptp.element Y tptp.k))) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) :rule cong :premises (t172.t2 t172.t3 t172.t4 t172.t5))
% 0.55/0.72 (step t172 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (= Y tptp.m) (= Y tptp.n) (not (tptp.element Y tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))))) :rule bind)
% 0.55/0.72 (step t173 (cl (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) :rule resolution :premises (t171 t172 a15))
% 0.55/0.72 (step t174 (cl (or (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.n (tptp.f tptp.k)) (not (tptp.element (tptp.f tptp.k) tptp.k)))) :rule resolution :premises (t170 t173))
% 0.55/0.72 (step t175 (cl (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)) :rule or_pos)
% 0.55/0.72 (step t176 (cl (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)))) :rule reordering :premises (t175))
% 0.55/0.72 (step t177 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t178)
% 0.55/0.72 (assume t178.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))
% 0.55/0.72 (step t178.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t178.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule or :premises (t178.t1))
% 0.55/0.72 (step t178.t3 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule resolution :premises (t178.t2 t178.a0))
% 0.55/0.72 (step t178 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule subproof :discharge (t178.a0))
% 0.55/0.72 (step t179 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule resolution :premises (t177 t178))
% 0.55/0.72 (step t180 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)))) :rule implies_neg2)
% 0.55/0.72 (step t181 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)))) :rule resolution :premises (t179 t180))
% 0.55/0.72 (step t182 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k)))) :rule contraction :premises (t181))
% 0.55/0.72 (step t183 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule implies :premises (t182))
% 0.55/0.72 (step t184 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t185 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t185.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t185.t2 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t185.t3 (cl (= (not (tptp.element Y tptp.m)) (not (tptp.element Y tptp.m)))) :rule refl)
% 0.55/0.72 (step t185.t4 (cl (= (tptp.element (tptp.f Y) Y) (tptp.element (tptp.f Y) Y))) :rule refl)
% 0.55/0.72 (step t185.t5 (cl (= (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) :rule cong :premises (t185.t2 t185.t3 t185.t4))
% 0.55/0.72 (step t185 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))) :rule bind)
% 0.55/0.72 (step t186 (cl (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) :rule resolution :premises (t184 t185 a6))
% 0.55/0.72 (step t187 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element (tptp.f tptp.k) tptp.k))) :rule resolution :premises (t183 t186))
% 0.55/0.72 (step t188 (cl (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))) :rule or_pos)
% 0.55/0.72 (step t189 (cl (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule reordering :premises (t188))
% 0.55/0.72 (step t190 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t191)
% 0.55/0.72 (assume t191.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))
% 0.55/0.72 (step t191.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t191.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule or :premises (t191.t1))
% 0.55/0.72 (step t191.t3 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t191.t2 t191.a0))
% 0.55/0.72 (step t191 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule subproof :discharge (t191.a0))
% 0.55/0.72 (step t192 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t190 t191))
% 0.55/0.72 (step t193 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t194 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t192 t193))
% 0.55/0.72 (step t195 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k))))) :rule contraction :premises (t194))
% 0.55/0.72 (step t196 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule implies :premises (t195))
% 0.55/0.72 (step t197 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t198 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t198.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t198.t2 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t198.t3 (cl (= (not (tptp.element Y tptp.m)) (not (tptp.element Y tptp.m)))) :rule refl)
% 0.55/0.72 (step t198.t4 (cl (= (tptp.element Y (tptp.f Y)) (tptp.element Y (tptp.f Y)))) :rule refl)
% 0.55/0.72 (step t198.t5 (cl (= (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) :rule cong :premises (t198.t2 t198.t3 t198.t4))
% 0.55/0.72 (step t198 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))) :rule bind)
% 0.55/0.72 (step t199 (cl (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) :rule resolution :premises (t197 t198 a5))
% 0.55/0.72 (step t200 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t196 t199))
% 0.55/0.72 (step t201 (cl (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))) :rule or_pos)
% 0.55/0.72 (step t202 (cl (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))))) :rule reordering :premises (t201))
% 0.55/0.72 (step t203 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t204)
% 0.55/0.72 (assume t204.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))))
% 0.55/0.72 (step t204.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t204.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule or :premises (t204.t1))
% 0.55/0.72 (step t204.t3 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t204.t2 t204.a0))
% 0.55/0.72 (step t204 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule subproof :discharge (t204.a0))
% 0.55/0.72 (step t205 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t203 t204))
% 0.55/0.72 (step t206 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))))) :rule implies_neg2)
% 0.55/0.72 (step t207 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))))) :rule resolution :premises (t205 t206))
% 0.55/0.72 (step t208 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k)))))) :rule contraction :premises (t207))
% 0.55/0.72 (step t209 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule implies :premises (t208))
% 0.55/0.72 (step t210 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) Y))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t211 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t211.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t211.t2 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t211.t3 (cl (= (not (tptp.element Y tptp.m)) (not (tptp.element Y tptp.m)))) :rule refl)
% 0.55/0.72 (step t211.t4 (cl (= (= (tptp.f Y) Y) (= Y (tptp.f Y)))) :rule all_simplify)
% 0.55/0.72 (step t211.t5 (cl (= (not (= (tptp.f Y) Y)) (not (= Y (tptp.f Y))))) :rule cong :premises (t211.t4))
% 0.55/0.72 (step t211.t6 (cl (= (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) Y))) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) :rule cong :premises (t211.t2 t211.t3 t211.t5))
% 0.55/0.72 (step t211 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))))) :rule bind)
% 0.55/0.72 (step t212 (cl (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) :rule resolution :premises (t210 t211 a4))
% 0.55/0.72 (step t213 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.k (tptp.f tptp.k))))) :rule resolution :premises (t209 t212))
% 0.55/0.72 (step t214 (cl (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))) :rule or_pos)
% 0.55/0.72 (step t215 (cl (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))))) :rule reordering :premises (t214))
% 0.55/0.72 (step t216 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t217)
% 0.55/0.72 (assume t217.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))))
% 0.55/0.72 (step t217.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t217.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule or :premises (t217.t1))
% 0.55/0.72 (step t217.t3 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule resolution :premises (t217.t2 t217.a0))
% 0.55/0.72 (step t217 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule subproof :discharge (t217.a0))
% 0.55/0.72 (step t218 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule resolution :premises (t216 t217))
% 0.55/0.72 (step t219 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) (not (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))))) :rule implies_neg2)
% 0.55/0.72 (step t220 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))))) :rule resolution :premises (t218 t219))
% 0.55/0.72 (step t221 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k)))))) :rule contraction :premises (t220))
% 0.55/0.72 (step t222 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule implies :premises (t221))
% 0.55/0.72 (step t223 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) tptp.m)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) tptp.m))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t224 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t224.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t224.t2 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t224.t3 (cl (= (not (tptp.element Y tptp.m)) (not (tptp.element Y tptp.m)))) :rule refl)
% 0.55/0.72 (step t224.t4 (cl (= (= (tptp.f Y) tptp.m) (= tptp.m (tptp.f Y)))) :rule all_simplify)
% 0.55/0.72 (step t224.t5 (cl (= (not (= (tptp.f Y) tptp.m)) (not (= tptp.m (tptp.f Y))))) :rule cong :premises (t224.t4))
% 0.55/0.72 (step t224.t6 (cl (= (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) tptp.m))) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) :rule cong :premises (t224.t2 t224.t3 t224.t5))
% 0.55/0.72 (step t224 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.m) (not (tptp.element Y tptp.m)) (not (= (tptp.f Y) tptp.m)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))))) :rule bind)
% 0.55/0.72 (step t225 (cl (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) :rule resolution :premises (t223 t224 a3))
% 0.55/0.72 (step t226 (cl (or (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (not (= tptp.m (tptp.f tptp.k))))) :rule resolution :premises (t222 t225))
% 0.55/0.72 (step t227 (cl (tptp.element tptp.k tptp.n) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) :rule resolution :premises (t161 t163 t174 t176 t187 t189 t200 t202 t213 t215 t226))
% 0.55/0.72 (step t228 (cl (tptp.element tptp.k tptp.n) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) :rule contraction :premises (t227))
% 0.55/0.72 (step t229 (cl (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k tptp.n)) :rule reordering :premises (t228))
% 0.55/0.72 (step t230 (cl (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) :rule resolution :premises (t78 t100 t101 t229))
% 0.55/0.72 (step t231 (cl (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (not (tptp.element tptp.k tptp.m))) :rule contraction :premises (t230))
% 0.55/0.72 (step t232 (cl (not (= (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (or (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))))) (not (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) (or (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t233 (cl (= (= (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m)) true) (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t234 (cl (not (= (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m)) true)) (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m))) :rule equiv1 :premises (t233))
% 0.55/0.72 (step t235 (cl (= (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m)) (= (tptp.element tptp.k tptp.m) (not (not (tptp.element tptp.k tptp.m)))))) :rule all_simplify)
% 0.55/0.72 (step t236 (cl (= (tptp.element tptp.k tptp.m) (tptp.element tptp.k tptp.m))) :rule refl)
% 0.55/0.72 (step t237 (cl (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m))) :rule all_simplify)
% 0.55/0.72 (step t238 (cl (= (= (tptp.element tptp.k tptp.m) (not (not (tptp.element tptp.k tptp.m)))) (= (tptp.element tptp.k tptp.m) (tptp.element tptp.k tptp.m)))) :rule cong :premises (t236 t237))
% 0.55/0.72 (step t239 (cl (= (= (tptp.element tptp.k tptp.m) (tptp.element tptp.k tptp.m)) true)) :rule all_simplify)
% 0.55/0.72 (step t240 (cl (= (= (tptp.element tptp.k tptp.m) (not (not (tptp.element tptp.k tptp.m)))) true)) :rule trans :premises (t238 t239))
% 0.55/0.72 (step t241 (cl (= (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m)) true)) :rule trans :premises (t235 t240))
% 0.55/0.72 (step t242 (cl (= (not (not (tptp.element tptp.k tptp.m))) (tptp.element tptp.k tptp.m))) :rule resolution :premises (t234 t241))
% 0.55/0.72 (step t243 (cl (= (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element tptp.k (tptp.g tptp.k))))) :rule refl)
% 0.55/0.72 (step t244 (cl (= (not (= tptp.m (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) :rule refl)
% 0.55/0.72 (step t245 (cl (= (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (or (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))))) :rule cong :premises (t242 t243 t244))
% 0.55/0.72 (step t246 (cl (not (= (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))))) (not (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t247 (cl (= (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))))) :rule refl)
% 0.55/0.72 (step t248 (cl (= (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))))) :rule equiv_simplify)
% 0.55/0.72 (step t249 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))))) :rule equiv2 :premises (t248))
% 0.55/0.72 (step t250 (cl (not (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule not_not)
% 0.55/0.72 (step t251 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t249 t250))
% 0.55/0.72 (step t252 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t253)
% 0.55/0.72 (assume t253.a0 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (assume t253.a1 (= tptp.m (tptp.g tptp.k)))
% 0.55/0.72 (assume t253.a2 (tptp.element tptp.k (tptp.g tptp.k)))
% 0.55/0.72 (step t253.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.55/0.72 (step t253.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.55/0.72 (step t253.t3 (cl (= (= (tptp.element tptp.k (tptp.g tptp.k)) true) (tptp.element tptp.k (tptp.g tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t253.t4 (cl (= (tptp.element tptp.k (tptp.g tptp.k)) true) (not (tptp.element tptp.k (tptp.g tptp.k)))) :rule equiv2 :premises (t253.t3))
% 0.55/0.72 (step t253.t5 (cl (= (tptp.element tptp.k (tptp.g tptp.k)) true)) :rule resolution :premises (t253.t4 t253.a2))
% 0.55/0.72 (step t253.t6 (cl (= true (tptp.element tptp.k (tptp.g tptp.k)))) :rule symm :premises (t253.t5))
% 0.55/0.72 (step t253.t7 (cl (= tptp.k tptp.k)) :rule refl)
% 0.55/0.72 (step t253.t8 (cl (= (tptp.g tptp.k) tptp.m)) :rule symm :premises (t253.a1))
% 0.55/0.72 (step t253.t9 (cl (= (tptp.element tptp.k (tptp.g tptp.k)) (tptp.element tptp.k tptp.m))) :rule cong :premises (t253.t7 t253.t8))
% 0.55/0.72 (step t253.t10 (cl (= (= (tptp.element tptp.k tptp.m) false) (not (tptp.element tptp.k tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t253.t11 (cl (= (tptp.element tptp.k tptp.m) false) (not (not (tptp.element tptp.k tptp.m)))) :rule equiv2 :premises (t253.t10))
% 0.55/0.72 (step t253.t12 (cl (not (not (not (tptp.element tptp.k tptp.m)))) (tptp.element tptp.k tptp.m)) :rule not_not)
% 0.55/0.72 (step t253.t13 (cl (= (tptp.element tptp.k tptp.m) false) (tptp.element tptp.k tptp.m)) :rule resolution :premises (t253.t11 t253.t12))
% 0.55/0.72 (step t253.t14 (cl (= (tptp.element tptp.k tptp.m) false)) :rule resolution :premises (t253.t13 t253.a0))
% 0.55/0.72 (step t253.t15 (cl (= true false)) :rule trans :premises (t253.t6 t253.t9 t253.t14))
% 0.55/0.72 (step t253.t16 (cl false) :rule resolution :premises (t253.t1 t253.t2 t253.t15))
% 0.55/0.72 (step t253 (cl (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.m (tptp.g tptp.k))) (not (tptp.element tptp.k (tptp.g tptp.k))) false) :rule subproof :discharge (t253.a0 t253.a1 t253.a2))
% 0.55/0.72 (step t254 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t255 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (= tptp.m (tptp.g tptp.k))) :rule and_pos)
% 0.55/0.72 (step t256 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (tptp.element tptp.k (tptp.g tptp.k))) :rule and_pos)
% 0.55/0.72 (step t257 (cl false (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t253 t254 t255 t256))
% 0.55/0.72 (step t258 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) false) :rule reordering :premises (t257))
% 0.55/0.72 (step t259 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) false) :rule contraction :premises (t258))
% 0.55/0.72 (step t260 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) false) :rule resolution :premises (t252 t259))
% 0.55/0.72 (step t261 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t262 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false)) :rule resolution :premises (t260 t261))
% 0.55/0.72 (step t263 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false)) :rule contraction :premises (t262))
% 0.55/0.72 (step t264 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))))) :rule implies_simplify)
% 0.55/0.72 (step t265 (cl (not (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false)) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule equiv1 :premises (t264))
% 0.55/0.72 (step t266 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t263 t265))
% 0.55/0.72 (step t267 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) false)) :rule resolution :premises (t251 t266))
% 0.55/0.72 (step t268 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) false))) :rule cong :premises (t247 t267))
% 0.55/0.72 (step t269 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) false) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))))) :rule all_simplify)
% 0.55/0.72 (step t270 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))))) :rule trans :premises (t268 t269))
% 0.55/0.72 (step t271 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t272)
% 0.55/0.72 (assume t272.a0 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (assume t272.a1 (tptp.element tptp.k (tptp.g tptp.k)))
% 0.55/0.72 (assume t272.a2 (= tptp.m (tptp.g tptp.k)))
% 0.55/0.72 (step t272.t1 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.m (tptp.g tptp.k))) (not (tptp.element tptp.k (tptp.g tptp.k)))) :rule and_neg)
% 0.55/0.72 (step t272.t2 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t272.t1 t272.a0 t272.a2 t272.a1))
% 0.55/0.72 (step t272 (cl (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule subproof :discharge (t272.a0 t272.a1 t272.a2))
% 0.55/0.72 (step t273 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t274 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (tptp.element tptp.k (tptp.g tptp.k))) :rule and_pos)
% 0.55/0.72 (step t275 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (= tptp.m (tptp.g tptp.k))) :rule and_pos)
% 0.55/0.72 (step t276 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))))) :rule resolution :premises (t272 t273 t274 t275))
% 0.55/0.72 (step t277 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule reordering :premises (t276))
% 0.55/0.72 (step t278 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule contraction :premises (t277))
% 0.55/0.72 (step t279 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t271 t278))
% 0.55/0.72 (step t280 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t281 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k)))) (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t279 t280))
% 0.55/0.72 (step t282 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m (tptp.g tptp.k)) (tptp.element tptp.k (tptp.g tptp.k))))) :rule contraction :premises (t281))
% 0.55/0.72 (step t283 (cl (not (and (not (tptp.element tptp.k tptp.m)) (tptp.element tptp.k (tptp.g tptp.k)) (= tptp.m (tptp.g tptp.k))))) :rule resolution :premises (t246 t270 t282))
% 0.55/0.72 (step t284 (cl (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) :rule not_and :premises (t283))
% 0.55/0.72 (step t285 (cl (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (not (not (not (tptp.element tptp.k tptp.m))))) :rule or_neg)
% 0.55/0.72 (step t286 (cl (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (not (not (tptp.element tptp.k (tptp.g tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t287 (cl (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (not (not (= tptp.m (tptp.g tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t288 (cl (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) :rule resolution :premises (t284 t285 t286 t287))
% 0.55/0.72 (step t289 (cl (or (not (not (tptp.element tptp.k tptp.m))) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) :rule contraction :premises (t288))
% 0.55/0.72 (step t290 (cl (or (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k))))) :rule resolution :premises (t232 t245 t289))
% 0.55/0.72 (step t291 (cl (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (= tptp.m (tptp.g tptp.k)))) :rule or :premises (t290))
% 0.55/0.72 (step t292 (cl (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))) :rule or_pos)
% 0.55/0.72 (step t293 (cl (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)) (= tptp.m (tptp.g tptp.k)) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))))) :rule reordering :premises (t292))
% 0.55/0.72 (step t294 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t295)
% 0.55/0.72 (assume t295.a0 (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))
% 0.55/0.72 (step t295.t1 (cl (or (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))))) :rule forall_inst :args ((:= Y tptp.k) (:= V1 (tptp.g tptp.k))))
% 0.55/0.72 (step t295.t2 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule or :premises (t295.t1))
% 0.55/0.72 (step t295.t3 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule resolution :premises (t295.t2 t295.a0))
% 0.55/0.72 (step t295 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule subproof :discharge (t295.a0))
% 0.55/0.72 (step t296 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule resolution :premises (t294 t295))
% 0.55/0.72 (step t297 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t298 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))))) :rule resolution :premises (t296 t297))
% 0.55/0.72 (step t299 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k))))) :rule contraction :premises (t298))
% 0.55/0.72 (step t300 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule implies :premises (t299))
% 0.55/0.72 (step t301 (cl (not (= (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= Y tptp.m) (tptp.element Y tptp.m) (= V1 tptp.m) (= V1 Y) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))) (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= Y tptp.m) (tptp.element Y tptp.m) (= V1 tptp.m) (= V1 Y) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t302 :args ((Y $$unsorted) (:= Y Y) (V1 $$unsorted) (:= V1 V1)))
% 0.55/0.72 (step t302.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t302.t2 (cl (= V1 V1)) :rule refl)
% 0.55/0.72 (step t302.t3 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t302.t4 (cl (= (tptp.element Y tptp.m) (tptp.element Y tptp.m))) :rule refl)
% 0.55/0.72 (step t302.t5 (cl (= (= V1 tptp.m) (= tptp.m V1))) :rule all_simplify)
% 0.55/0.72 (step t302.t6 (cl (= (= V1 Y) (= Y V1))) :rule all_simplify)
% 0.55/0.72 (step t302.t7 (cl (= (not (tptp.element Y V1)) (not (tptp.element Y V1)))) :rule refl)
% 0.55/0.72 (step t302.t8 (cl (= (not (tptp.element V1 Y)) (not (tptp.element V1 Y)))) :rule refl)
% 0.55/0.72 (step t302.t9 (cl (= (or (= Y tptp.m) (tptp.element Y tptp.m) (= V1 tptp.m) (= V1 Y) (not (tptp.element Y V1)) (not (tptp.element V1 Y))) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule cong :premises (t302.t3 t302.t4 t302.t5 t302.t6 t302.t7 t302.t8))
% 0.55/0.72 (step t302 (cl (= (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= Y tptp.m) (tptp.element Y tptp.m) (= V1 tptp.m) (= V1 Y) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))) :rule bind)
% 0.55/0.72 (step t303 (cl (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule resolution :premises (t301 t302 a7))
% 0.55/0.72 (step t304 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m (tptp.g tptp.k)) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (not (tptp.element (tptp.g tptp.k) tptp.k)))) :rule resolution :premises (t300 t303))
% 0.55/0.72 (step t305 (cl (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)) :rule or_pos)
% 0.55/0.72 (step t306 (cl (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)))) :rule reordering :premises (t305))
% 0.55/0.72 (step t307 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t308)
% 0.55/0.72 (assume t308.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))))
% 0.55/0.72 (step t308.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t308.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule or :premises (t308.t1))
% 0.55/0.72 (step t308.t3 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule resolution :premises (t308.t2 t308.a0))
% 0.55/0.72 (step t308 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule subproof :discharge (t308.a0))
% 0.55/0.72 (step t309 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule resolution :premises (t307 t308))
% 0.55/0.72 (step t310 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)))) :rule implies_neg2)
% 0.55/0.72 (step t311 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)))) :rule resolution :premises (t309 t310))
% 0.55/0.72 (step t312 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k)))) :rule contraction :premises (t311))
% 0.55/0.72 (step t313 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule implies :premises (t312))
% 0.55/0.72 (step t314 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t315 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t315.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t315.t2 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t315.t3 (cl (= (tptp.element Y tptp.n) (tptp.element Y tptp.n))) :rule refl)
% 0.55/0.72 (step t315.t4 (cl (= (tptp.element (tptp.g Y) Y) (tptp.element (tptp.g Y) Y))) :rule refl)
% 0.55/0.72 (step t315.t5 (cl (= (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) :rule cong :premises (t315.t2 t315.t3 t315.t4))
% 0.55/0.72 (step t315 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))))) :rule bind)
% 0.55/0.72 (step t316 (cl (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) :rule resolution :premises (t314 t315 a11))
% 0.55/0.72 (step t317 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element (tptp.g tptp.k) tptp.k))) :rule resolution :premises (t313 t316))
% 0.55/0.72 (step t318 (cl (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.k (tptp.g tptp.k)) (not (tptp.element tptp.k (tptp.g tptp.k))) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n)) :rule resolution :premises (t291 t293 t304 t306 t317))
% 0.55/0.72 (step t319 (cl (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k (tptp.g tptp.k))) (= tptp.m tptp.k) (= tptp.k (tptp.g tptp.k)) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n)) :rule contraction :premises (t318))
% 0.55/0.72 (step t320 (cl (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))) :rule or_pos)
% 0.55/0.72 (step t321 (cl (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))))) :rule reordering :premises (t320))
% 0.55/0.72 (step t322 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t323)
% 0.55/0.72 (assume t323.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))))
% 0.55/0.72 (step t323.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t323.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule or :premises (t323.t1))
% 0.55/0.72 (step t323.t3 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t323.t2 t323.a0))
% 0.55/0.72 (step t323 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule subproof :discharge (t323.a0))
% 0.55/0.72 (step t324 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t322 t323))
% 0.55/0.72 (step t325 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t326 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t324 t325))
% 0.55/0.72 (step t327 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k))))) :rule contraction :premises (t326))
% 0.55/0.72 (step t328 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule implies :premises (t327))
% 0.55/0.72 (step t329 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t330 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t330.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t330.t2 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t330.t3 (cl (= (tptp.element Y tptp.n) (tptp.element Y tptp.n))) :rule refl)
% 0.55/0.72 (step t330.t4 (cl (= (tptp.element Y (tptp.g Y)) (tptp.element Y (tptp.g Y)))) :rule refl)
% 0.55/0.72 (step t330.t5 (cl (= (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) :rule cong :premises (t330.t2 t330.t3 t330.t4))
% 0.55/0.72 (step t330 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y)))))) :rule bind)
% 0.55/0.72 (step t331 (cl (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element Y (tptp.g Y))))) :rule resolution :premises (t329 t330 a10))
% 0.55/0.72 (step t332 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (tptp.element tptp.k (tptp.g tptp.k)))) :rule resolution :premises (t328 t331))
% 0.55/0.72 (step t333 (cl (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))) :rule or_pos)
% 0.55/0.72 (step t334 (cl (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))))) :rule reordering :premises (t333))
% 0.55/0.72 (step t335 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t336)
% 0.55/0.72 (assume t336.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))))
% 0.55/0.72 (step t336.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))))) :rule forall_inst :args ((:= Y tptp.k)))
% 0.55/0.72 (step t336.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule or :premises (t336.t1))
% 0.55/0.72 (step t336.t3 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t336.t2 t336.a0))
% 0.55/0.72 (step t336 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule subproof :discharge (t336.a0))
% 0.55/0.72 (step t337 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t335 t336))
% 0.55/0.72 (step t338 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) (not (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))))) :rule implies_neg2)
% 0.55/0.72 (step t339 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))))) :rule resolution :premises (t337 t338))
% 0.55/0.72 (step t340 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k)))))) :rule contraction :premises (t339))
% 0.55/0.72 (step t341 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule implies :premises (t340))
% 0.55/0.72 (step t342 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) Y))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t343 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t343.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t343.t2 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t343.t3 (cl (= (tptp.element Y tptp.n) (tptp.element Y tptp.n))) :rule refl)
% 0.55/0.72 (step t343.t4 (cl (= (= (tptp.g Y) Y) (= Y (tptp.g Y)))) :rule all_simplify)
% 0.55/0.72 (step t343.t5 (cl (= (not (= (tptp.g Y) Y)) (not (= Y (tptp.g Y))))) :rule cong :premises (t343.t4))
% 0.55/0.72 (step t343.t6 (cl (= (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) Y))) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) :rule cong :premises (t343.t2 t343.t3 t343.t5))
% 0.55/0.72 (step t343 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) Y)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))))) :rule bind)
% 0.55/0.72 (step t344 (cl (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) :rule resolution :premises (t342 t343 a9))
% 0.55/0.72 (step t345 (cl (or (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (not (= tptp.k (tptp.g tptp.k))))) :rule resolution :premises (t341 t344))
% 0.55/0.72 (step t346 (cl (tptp.element tptp.k tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n)) :rule resolution :premises (t319 t321 t332 t334 t345))
% 0.55/0.72 (step t347 (cl (tptp.element tptp.k tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k) (tptp.element tptp.k tptp.n)) :rule contraction :premises (t346))
% 0.55/0.72 (step t348 (cl (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))) :rule or_pos)
% 0.55/0.72 (step t349 (cl (= tptp.n tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.k)) (tptp.element tptp.k tptp.m) (not (tptp.element tptp.k tptp.n)) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule reordering :premises (t348))
% 0.55/0.72 (step t350 (cl (not (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))))) (not (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t351 (cl (= (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))) :rule refl)
% 0.55/0.72 (step t352 (cl (= (= tptp.m tptp.k) (= tptp.m tptp.k))) :rule refl)
% 0.55/0.72 (step t353 (cl (= (= tptp.m tptp.n) (= tptp.n tptp.m))) :rule all_simplify)
% 0.55/0.72 (step t354 (cl (= (= tptp.k tptp.n) (= tptp.n tptp.k))) :rule all_simplify)
% 0.55/0.72 (step t355 (cl (= (not (tptp.element tptp.n tptp.k)) (not (tptp.element tptp.n tptp.k)))) :rule refl)
% 0.55/0.72 (step t356 (cl (= (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule cong :premises (t352 t236 t353 t354 t82 t355))
% 0.55/0.72 (step t357 (cl (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))))) :rule cong :premises (t351 t356))
% 0.55/0.72 (step t358 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t359)
% 0.55/0.72 (assume t359.a0 (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))
% 0.55/0.72 (step t359.t1 (cl (or (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule forall_inst :args ((:= Y tptp.k) (:= V1 tptp.n)))
% 0.55/0.72 (step t359.t2 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule or :premises (t359.t1))
% 0.55/0.72 (step t359.t3 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule resolution :premises (t359.t2 t359.a0))
% 0.55/0.72 (step t359 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule subproof :discharge (t359.a0))
% 0.55/0.72 (step t360 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule resolution :premises (t358 t359))
% 0.55/0.72 (step t361 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t362 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule resolution :premises (t360 t361))
% 0.55/0.72 (step t363 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule contraction :premises (t362))
% 0.55/0.72 (step t364 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k))))) :rule resolution :premises (t350 t357 t363))
% 0.55/0.72 (step t365 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule implies :premises (t364))
% 0.55/0.72 (step t366 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.k tptp.n)) (not (tptp.element tptp.n tptp.k)))) :rule resolution :premises (t365 t303))
% 0.55/0.72 (step t367 (cl (not (= tptp.n tptp.m))) :rule not_symm :premises (a0))
% 0.55/0.72 (step t368 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k))) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)))) (not (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k)))) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t369 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t369.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t369.t2 (cl (= (= Y tptp.k) (= tptp.k Y))) :rule all_simplify)
% 0.55/0.72 (step t369.t3 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t369.t4 (cl (= (not (= Y tptp.n)) (not (= tptp.n Y)))) :rule cong :premises (t369.t3))
% 0.55/0.72 (step t369.t5 (cl (= (tptp.element Y tptp.k) (tptp.element Y tptp.k))) :rule refl)
% 0.55/0.72 (step t369.t6 (cl (= (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k)) (or (= tptp.k Y) (not (= tptp.n Y)) (tptp.element Y tptp.k)))) :rule cong :premises (t369.t2 t369.t4 t369.t5))
% 0.55/0.72 (step t369 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.n Y)) (tptp.element Y tptp.k))))) :rule bind)
% 0.55/0.72 (step t370 (cl (= (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.n Y)) (tptp.element Y tptp.k))) (or (= tptp.k tptp.n) (not (= tptp.n tptp.n)) (tptp.element tptp.n tptp.k)))) :rule all_simplify)
% 0.55/0.72 (step t371 (cl (= (= tptp.n tptp.n) true)) :rule all_simplify)
% 0.55/0.72 (step t372 (cl (= (not (= tptp.n tptp.n)) (not true))) :rule cong :premises (t371))
% 0.55/0.72 (step t373 (cl (= (not true) false)) :rule all_simplify)
% 0.55/0.72 (step t374 (cl (= (not (= tptp.n tptp.n)) false)) :rule trans :premises (t372 t373))
% 0.55/0.72 (step t375 (cl (= (tptp.element tptp.n tptp.k) (tptp.element tptp.n tptp.k))) :rule refl)
% 0.55/0.72 (step t376 (cl (= (or (= tptp.k tptp.n) (not (= tptp.n tptp.n)) (tptp.element tptp.n tptp.k)) (or (= tptp.n tptp.k) false (tptp.element tptp.n tptp.k)))) :rule cong :premises (t354 t374 t375))
% 0.55/0.72 (step t377 (cl (= (or (= tptp.n tptp.k) false (tptp.element tptp.n tptp.k)) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)))) :rule all_simplify)
% 0.55/0.72 (step t378 (cl (= (or (= tptp.k tptp.n) (not (= tptp.n tptp.n)) (tptp.element tptp.n tptp.k)) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)))) :rule trans :premises (t376 t377))
% 0.55/0.72 (step t379 (cl (= (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.n Y)) (tptp.element Y tptp.k))) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)))) :rule trans :premises (t370 t378))
% 0.55/0.72 (step t380 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.n)) (tptp.element Y tptp.k))) (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)))) :rule trans :premises (t369 t379))
% 0.55/0.72 (step t381 (cl (or (= tptp.n tptp.k) (tptp.element tptp.n tptp.k))) :rule resolution :premises (t368 t380 a14))
% 0.55/0.72 (step t382 (cl (= tptp.n tptp.k) (tptp.element tptp.n tptp.k)) :rule or :premises (t381))
% 0.55/0.72 (step t383 (cl (tptp.element tptp.n tptp.k) (= tptp.n tptp.k)) :rule reordering :premises (t382))
% 0.55/0.72 (step t384 (cl (tptp.element tptp.k tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.k) (= tptp.n tptp.k) (tptp.element tptp.k tptp.m) (= tptp.n tptp.k)) :rule resolution :premises (t347 t349 t366 t367 t383))
% 0.55/0.72 (step t385 (cl (tptp.element tptp.k tptp.m) (= tptp.m tptp.k) (= tptp.n tptp.k)) :rule contraction :premises (t384))
% 0.55/0.72 (step t386 (cl (not (= (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.k tptp.m)))) (not (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m))))) (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.k tptp.m))) :rule equiv_pos2)
% 0.55/0.72 (step t387 (cl (= (not (tptp.element tptp.m tptp.k)) (not (tptp.element tptp.m tptp.k)))) :rule refl)
% 0.55/0.72 (step t388 (cl (= (not (= tptp.m tptp.k)) (not (= tptp.m tptp.k)))) :rule refl)
% 0.55/0.72 (step t389 (cl (= (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.k tptp.m)))) :rule cong :premises (t387 t388 t242))
% 0.55/0.72 (step t390 (cl (not (= (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))))) (not (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))))) :rule equiv_pos2)
% 0.55/0.72 (step t391 (cl (= (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))))) :rule refl)
% 0.55/0.72 (step t392 (cl (= (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))))) :rule equiv_simplify)
% 0.55/0.72 (step t393 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))))) :rule equiv2 :premises (t392))
% 0.55/0.72 (step t394 (cl (not (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule not_not)
% 0.55/0.72 (step t395 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule resolution :premises (t393 t394))
% 0.55/0.72 (step t396 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t397)
% 0.55/0.72 (assume t397.a0 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (assume t397.a1 (= tptp.m tptp.k))
% 0.55/0.72 (assume t397.a2 (tptp.element tptp.m tptp.k))
% 0.55/0.72 (step t397.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.55/0.72 (step t397.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.55/0.72 (step t397.t3 (cl (= (= (tptp.element tptp.m tptp.k) true) (tptp.element tptp.m tptp.k))) :rule equiv_simplify)
% 0.55/0.72 (step t397.t4 (cl (= (tptp.element tptp.m tptp.k) true) (not (tptp.element tptp.m tptp.k))) :rule equiv2 :premises (t397.t3))
% 0.55/0.72 (step t397.t5 (cl (= (tptp.element tptp.m tptp.k) true)) :rule resolution :premises (t397.t4 t397.a2))
% 0.55/0.72 (step t397.t6 (cl (= true (tptp.element tptp.m tptp.k))) :rule symm :premises (t397.t5))
% 0.55/0.72 (step t397.t7 (cl (= tptp.k tptp.m)) :rule symm :premises (t397.a1))
% 0.55/0.72 (step t397.t8 (cl (= (tptp.element tptp.m tptp.k) (tptp.element tptp.k tptp.m))) :rule cong :premises (t397.a1 t397.t7))
% 0.55/0.72 (step t397.t9 (cl (= (= (tptp.element tptp.k tptp.m) false) (not (tptp.element tptp.k tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t397.t10 (cl (= (tptp.element tptp.k tptp.m) false) (not (not (tptp.element tptp.k tptp.m)))) :rule equiv2 :premises (t397.t9))
% 0.55/0.72 (step t397.t11 (cl (not (not (not (tptp.element tptp.k tptp.m)))) (tptp.element tptp.k tptp.m)) :rule not_not)
% 0.55/0.72 (step t397.t12 (cl (= (tptp.element tptp.k tptp.m) false) (tptp.element tptp.k tptp.m)) :rule resolution :premises (t397.t10 t397.t11))
% 0.55/0.72 (step t397.t13 (cl (= (tptp.element tptp.k tptp.m) false)) :rule resolution :premises (t397.t12 t397.a0))
% 0.55/0.72 (step t397.t14 (cl (= true false)) :rule trans :premises (t397.t6 t397.t8 t397.t13))
% 0.55/0.72 (step t397.t15 (cl false) :rule resolution :premises (t397.t1 t397.t2 t397.t14))
% 0.55/0.72 (step t397 (cl (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.m tptp.k)) (not (tptp.element tptp.m tptp.k)) false) :rule subproof :discharge (t397.a0 t397.a1 t397.a2))
% 0.55/0.72 (step t398 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t399 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t400 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (tptp.element tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t401 (cl false (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t397 t398 t399 t400))
% 0.55/0.72 (step t402 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) false) :rule reordering :premises (t401))
% 0.55/0.72 (step t403 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) false) :rule contraction :premises (t402))
% 0.55/0.72 (step t404 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) false) :rule resolution :premises (t396 t403))
% 0.55/0.72 (step t405 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t406 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false)) :rule resolution :premises (t404 t405))
% 0.55/0.72 (step t407 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false)) :rule contraction :premises (t406))
% 0.55/0.72 (step t408 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))))) :rule implies_simplify)
% 0.55/0.72 (step t409 (cl (not (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false)) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule equiv1 :premises (t408))
% 0.55/0.72 (step t410 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t407 t409))
% 0.55/0.72 (step t411 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) false)) :rule resolution :premises (t395 t410))
% 0.55/0.72 (step t412 (cl (= (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) false))) :rule cong :premises (t391 t411))
% 0.55/0.72 (step t413 (cl (= (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) false) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))))) :rule all_simplify)
% 0.55/0.72 (step t414 (cl (= (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))))) :rule trans :premises (t412 t413))
% 0.55/0.72 (step t415 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t416)
% 0.55/0.72 (assume t416.a0 (tptp.element tptp.m tptp.k))
% 0.55/0.72 (assume t416.a1 (= tptp.m tptp.k))
% 0.55/0.72 (assume t416.a2 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (step t416.t1 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.m tptp.k)) (not (tptp.element tptp.m tptp.k))) :rule and_neg)
% 0.55/0.72 (step t416.t2 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule resolution :premises (t416.t1 t416.a2 t416.a1 t416.a0))
% 0.55/0.72 (step t416 (cl (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule subproof :discharge (t416.a0 t416.a1 t416.a2))
% 0.55/0.72 (step t417 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (tptp.element tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t418 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t419 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t420 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t416 t417 t418 t419))
% 0.55/0.72 (step t421 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule reordering :premises (t420))
% 0.55/0.72 (step t422 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule contraction :premises (t421))
% 0.55/0.72 (step t423 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule resolution :premises (t415 t422))
% 0.55/0.72 (step t424 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule implies_neg2)
% 0.55/0.72 (step t425 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t423 t424))
% 0.55/0.72 (step t426 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule contraction :premises (t425))
% 0.55/0.72 (step t427 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t390 t414 t426))
% 0.55/0.72 (step t428 (cl (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) :rule not_and :premises (t427))
% 0.55/0.72 (step t429 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (tptp.element tptp.m tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t430 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (= tptp.m tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t431 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (not (tptp.element tptp.k tptp.m))))) :rule or_neg)
% 0.55/0.72 (step t432 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t428 t429 t430 t431))
% 0.55/0.72 (step t433 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (not (tptp.element tptp.k tptp.m))))) :rule contraction :premises (t432))
% 0.55/0.72 (step t434 (cl (or (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.k tptp.m))) :rule resolution :premises (t386 t389 t433))
% 0.55/0.72 (step t435 (cl (not (tptp.element tptp.m tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.k tptp.m)) :rule or :premises (t434))
% 0.55/0.72 (step t436 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.m tptp.k)) (tptp.element tptp.k tptp.m)) :rule reordering :premises (t435))
% 0.55/0.72 (step t437 (cl (tptp.element tptp.k tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (tptp.element tptp.k tptp.m)) :rule resolution :premises (t385 t436))
% 0.55/0.72 (step t438 (cl (tptp.element tptp.k tptp.m) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k))) :rule contraction :premises (t437))
% 0.55/0.72 (step t439 (cl (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (tptp.element tptp.k tptp.m)) :rule reordering :premises (t438))
% 0.55/0.72 (step t440 (cl (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k)) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k))) :rule resolution :premises (t231 t439))
% 0.55/0.72 (step t441 (cl (= tptp.m tptp.k) (= tptp.n tptp.k) (not (tptp.element tptp.m tptp.k))) :rule contraction :premises (t440))
% 0.55/0.72 (step t442 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k))) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) (not (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k)))) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t443 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t443.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t443.t2 (cl (= (= Y tptp.k) (= tptp.k Y))) :rule all_simplify)
% 0.55/0.72 (step t443.t3 (cl (= (= Y tptp.m) (= tptp.m Y))) :rule all_simplify)
% 0.55/0.72 (step t443.t4 (cl (= (not (= Y tptp.m)) (not (= tptp.m Y)))) :rule cong :premises (t443.t3))
% 0.55/0.72 (step t443.t5 (cl (= (tptp.element Y tptp.k) (tptp.element Y tptp.k))) :rule refl)
% 0.55/0.72 (step t443.t6 (cl (= (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k)) (or (= tptp.k Y) (not (= tptp.m Y)) (tptp.element Y tptp.k)))) :rule cong :premises (t443.t2 t443.t4 t443.t5))
% 0.55/0.72 (step t443 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.m Y)) (tptp.element Y tptp.k))))) :rule bind)
% 0.55/0.72 (step t444 (cl (= (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.m Y)) (tptp.element Y tptp.k))) (or (= tptp.k tptp.m) (not (= tptp.m tptp.m)) (tptp.element tptp.m tptp.k)))) :rule all_simplify)
% 0.55/0.72 (step t445 (cl (= (= tptp.m tptp.m) true)) :rule all_simplify)
% 0.55/0.72 (step t446 (cl (= (not (= tptp.m tptp.m)) (not true))) :rule cong :premises (t445))
% 0.55/0.72 (step t447 (cl (= (not (= tptp.m tptp.m)) false)) :rule trans :premises (t446 t373))
% 0.55/0.72 (step t448 (cl (= (tptp.element tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule refl)
% 0.55/0.72 (step t449 (cl (= (or (= tptp.k tptp.m) (not (= tptp.m tptp.m)) (tptp.element tptp.m tptp.k)) (or (= tptp.m tptp.k) false (tptp.element tptp.m tptp.k)))) :rule cong :premises (t84 t447 t448))
% 0.55/0.72 (step t450 (cl (= (or (= tptp.m tptp.k) false (tptp.element tptp.m tptp.k)) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule all_simplify)
% 0.55/0.72 (step t451 (cl (= (or (= tptp.k tptp.m) (not (= tptp.m tptp.m)) (tptp.element tptp.m tptp.k)) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule trans :premises (t449 t450))
% 0.55/0.72 (step t452 (cl (= (forall ((Y $$unsorted)) (or (= tptp.k Y) (not (= tptp.m Y)) (tptp.element Y tptp.k))) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule trans :premises (t444 t451))
% 0.55/0.72 (step t453 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.k) (not (= Y tptp.m)) (tptp.element Y tptp.k))) (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)))) :rule trans :premises (t443 t452))
% 0.55/0.72 (step t454 (cl (or (= tptp.m tptp.k) (tptp.element tptp.m tptp.k))) :rule resolution :premises (t442 t453 a13))
% 0.55/0.72 (step t455 (cl (= tptp.m tptp.k) (tptp.element tptp.m tptp.k)) :rule or :premises (t454))
% 0.55/0.72 (step t456 (cl (tptp.element tptp.m tptp.k) (= tptp.m tptp.k)) :rule reordering :premises (t455))
% 0.55/0.72 (step t457 (cl (= tptp.m tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.k)) :rule resolution :premises (t441 t456))
% 0.55/0.72 (step t458 (cl (= tptp.m tptp.k) (= tptp.n tptp.k)) :rule contraction :premises (t457))
% 0.55/0.72 (step t459 (cl (not (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))) :rule or_pos)
% 0.55/0.72 (step t460 (cl (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (= tptp.k (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)) (not (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))))) :rule reordering :premises (t459))
% 0.55/0.72 (step t461 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t462)
% 0.55/0.72 (assume t462.a0 (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))))
% 0.55/0.72 (step t462.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))))) :rule forall_inst :args ((:= Y (tptp.f tptp.n))))
% 0.55/0.72 (step t462.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule or :premises (t462.t1))
% 0.55/0.72 (step t462.t3 (cl (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule resolution :premises (t462.t2 t462.a0))
% 0.55/0.72 (step t462 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule subproof :discharge (t462.a0))
% 0.55/0.72 (step t463 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule resolution :premises (t461 t462))
% 0.55/0.72 (step t464 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) (not (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t465 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))))) :rule resolution :premises (t463 t464))
% 0.55/0.72 (step t466 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k)))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k))))) :rule contraction :premises (t465))
% 0.55/0.72 (step t467 (cl (not (forall ((Y $$unsorted)) (or (= tptp.k Y) (= tptp.m Y) (= tptp.n Y) (not (tptp.element Y tptp.k))))) (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule implies :premises (t466))
% 0.55/0.72 (step t468 (cl (or (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.k)))) :rule resolution :premises (t467 t173))
% 0.55/0.72 (step t469 (cl (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (not (= tptp.m tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.m))) :rule and_neg)
% 0.55/0.72 (step t470 (cl (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t471)
% 0.55/0.72 (assume t471.a0 (= tptp.m tptp.k))
% 0.55/0.72 (assume t471.a1 (tptp.element (tptp.f tptp.n) tptp.m))
% 0.55/0.72 (step t471.t1 (cl (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t471.t2)
% 0.55/0.72 (assume t471.t2.a0 (tptp.element (tptp.f tptp.n) tptp.m))
% 0.55/0.72 (assume t471.t2.a1 (= tptp.m tptp.k))
% 0.55/0.72 (step t471.t2.t1 (cl (= (= (tptp.element (tptp.f tptp.n) tptp.k) true) (tptp.element (tptp.f tptp.n) tptp.k))) :rule equiv_simplify)
% 0.55/0.72 (step t471.t2.t2 (cl (not (= (tptp.element (tptp.f tptp.n) tptp.k) true)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule equiv1 :premises (t471.t2.t1))
% 0.55/0.72 (step t471.t2.t3 (cl (= (tptp.f tptp.n) (tptp.f tptp.n))) :rule refl)
% 0.55/0.72 (step t471.t2.t4 (cl (= tptp.k tptp.m)) :rule symm :premises (t471.t2.a1))
% 0.55/0.72 (step t471.t2.t5 (cl (= (tptp.element (tptp.f tptp.n) tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) :rule cong :premises (t471.t2.t3 t471.t2.t4))
% 0.55/0.72 (step t471.t2.t6 (cl (= (= (tptp.element (tptp.f tptp.n) tptp.m) true) (tptp.element (tptp.f tptp.n) tptp.m))) :rule equiv_simplify)
% 0.55/0.72 (step t471.t2.t7 (cl (= (tptp.element (tptp.f tptp.n) tptp.m) true) (not (tptp.element (tptp.f tptp.n) tptp.m))) :rule equiv2 :premises (t471.t2.t6))
% 0.55/0.72 (step t471.t2.t8 (cl (= (tptp.element (tptp.f tptp.n) tptp.m) true)) :rule resolution :premises (t471.t2.t7 t471.t2.a0))
% 0.55/0.72 (step t471.t2.t9 (cl (= (tptp.element (tptp.f tptp.n) tptp.k) true)) :rule trans :premises (t471.t2.t5 t471.t2.t8))
% 0.55/0.72 (step t471.t2.t10 (cl (tptp.element (tptp.f tptp.n) tptp.k)) :rule resolution :premises (t471.t2.t2 t471.t2.t9))
% 0.55/0.72 (step t471.t2 (cl (not (tptp.element (tptp.f tptp.n) tptp.m)) (not (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule subproof :discharge (t471.t2.a0 t471.t2.a1))
% 0.55/0.72 (step t471.t3 (cl (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (tptp.element (tptp.f tptp.n) tptp.m)) :rule and_pos)
% 0.55/0.72 (step t471.t4 (cl (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t471.t5 (cl (tptp.element (tptp.f tptp.n) tptp.k) (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)))) :rule resolution :premises (t471.t2 t471.t3 t471.t4))
% 0.55/0.72 (step t471.t6 (cl (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule reordering :premises (t471.t5))
% 0.55/0.72 (step t471.t7 (cl (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule contraction :premises (t471.t6))
% 0.55/0.72 (step t471.t8 (cl (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule resolution :premises (t471.t1 t471.t7))
% 0.55/0.72 (step t471.t9 (cl (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.k))) :rule implies_neg2)
% 0.55/0.72 (step t471.t10 (cl (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k))) :rule resolution :premises (t471.t8 t471.t9))
% 0.55/0.72 (step t471.t11 (cl (=> (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k))) :rule contraction :premises (t471.t10))
% 0.55/0.72 (step t471.t12 (cl (not (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule implies :premises (t471.t11))
% 0.55/0.72 (step t471.t13 (cl (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.m)) (not (= tptp.m tptp.k))) :rule and_neg)
% 0.55/0.72 (step t471.t14 (cl (and (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.k))) :rule resolution :premises (t471.t13 t471.a1 t471.a0))
% 0.55/0.72 (step t471.t15 (cl (tptp.element (tptp.f tptp.n) tptp.k)) :rule resolution :premises (t471.t12 t471.t14))
% 0.55/0.72 (step t471 (cl (not (= tptp.m tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule subproof :discharge (t471.a0 t471.a1))
% 0.55/0.72 (step t472 (cl (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t473 (cl (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (tptp.element (tptp.f tptp.n) tptp.m)) :rule and_pos)
% 0.55/0.72 (step t474 (cl (tptp.element (tptp.f tptp.n) tptp.k) (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)))) :rule resolution :premises (t471 t472 t473))
% 0.55/0.72 (step t475 (cl (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule reordering :premises (t474))
% 0.55/0.72 (step t476 (cl (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule contraction :premises (t475))
% 0.55/0.72 (step t477 (cl (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule resolution :premises (t470 t476))
% 0.55/0.72 (step t478 (cl (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.k))) :rule implies_neg2)
% 0.55/0.72 (step t479 (cl (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k))) :rule resolution :premises (t477 t478))
% 0.55/0.72 (step t480 (cl (=> (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k))) :rule contraction :premises (t479))
% 0.55/0.72 (step t481 (cl (not (and (= tptp.m tptp.k) (tptp.element (tptp.f tptp.n) tptp.m))) (tptp.element (tptp.f tptp.n) tptp.k)) :rule implies :premises (t480))
% 0.55/0.72 (step t482 (cl (not (= tptp.m tptp.k)) (not (tptp.element (tptp.f tptp.n) tptp.m)) (tptp.element (tptp.f tptp.n) tptp.k)) :rule resolution :premises (t469 t481))
% 0.55/0.72 (step t483 (cl (not (= (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (or (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (not (= tptp.k (tptp.f tptp.n)))))) (not (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n))))) (or (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (not (= tptp.k (tptp.f tptp.n))))) :rule equiv_pos2)
% 0.55/0.72 (step t484 (cl (= (= (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n))) true) (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n))))) :rule equiv_simplify)
% 0.55/0.72 (step t485 (cl (not (= (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n))) true)) (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n)))) :rule equiv1 :premises (t484))
% 0.55/0.72 (step t486 (cl (= (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n))) (= (= tptp.m (tptp.f tptp.n)) (not (not (= tptp.m (tptp.f tptp.n))))))) :rule all_simplify)
% 0.55/0.72 (step t487 (cl (= (= tptp.m (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)))) :rule refl)
% 0.55/0.72 (step t488 (cl (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n)))) :rule all_simplify)
% 0.55/0.72 (step t489 (cl (= (= (= tptp.m (tptp.f tptp.n)) (not (not (= tptp.m (tptp.f tptp.n))))) (= (= tptp.m (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n))))) :rule cong :premises (t487 t488))
% 0.55/0.72 (step t490 (cl (= (= (= tptp.m (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n))) true)) :rule all_simplify)
% 0.55/0.72 (step t491 (cl (= (= (= tptp.m (tptp.f tptp.n)) (not (not (= tptp.m (tptp.f tptp.n))))) true)) :rule trans :premises (t489 t490))
% 0.55/0.72 (step t492 (cl (= (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n))) true)) :rule trans :premises (t486 t491))
% 0.55/0.72 (step t493 (cl (= (not (not (= tptp.m (tptp.f tptp.n)))) (= tptp.m (tptp.f tptp.n)))) :rule resolution :premises (t485 t492))
% 0.55/0.72 (step t494 (cl (= (not (= tptp.k (tptp.f tptp.n))) (not (= tptp.k (tptp.f tptp.n))))) :rule refl)
% 0.55/0.72 (step t495 (cl (= (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (or (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (not (= tptp.k (tptp.f tptp.n)))))) :rule cong :premises (t388 t493 t494))
% 0.55/0.72 (step t496 (cl (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n))))) :rule and_neg)
% 0.55/0.72 (step t497 (cl (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t498)
% 0.55/0.72 (assume t498.a0 (= tptp.m tptp.k))
% 0.55/0.72 (assume t498.a1 (not (= tptp.m (tptp.f tptp.n))))
% 0.55/0.72 (step t498.t1 (cl (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n)))) (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t498.t2)
% 0.55/0.72 (assume t498.t2.a0 (not (= tptp.m (tptp.f tptp.n))))
% 0.55/0.72 (assume t498.t2.a1 (= tptp.m tptp.k))
% 0.55/0.72 (step t498.t2.t1 (cl (= (= (= tptp.k (tptp.f tptp.n)) false) (not (= tptp.k (tptp.f tptp.n))))) :rule equiv_simplify)
% 0.55/0.72 (step t498.t2.t2 (cl (not (= (= tptp.k (tptp.f tptp.n)) false)) (not (= tptp.k (tptp.f tptp.n)))) :rule equiv1 :premises (t498.t2.t1))
% 0.55/0.72 (step t498.t2.t3 (cl (= tptp.k tptp.m)) :rule symm :premises (t498.t2.a1))
% 0.55/0.72 (step t498.t2.t4 (cl (= (tptp.f tptp.n) (tptp.f tptp.n))) :rule refl)
% 0.55/0.72 (step t498.t2.t5 (cl (= (= tptp.k (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)))) :rule cong :premises (t498.t2.t3 t498.t2.t4))
% 0.55/0.72 (step t498.t2.t6 (cl (= (= (= tptp.m (tptp.f tptp.n)) false) (not (= tptp.m (tptp.f tptp.n))))) :rule equiv_simplify)
% 0.55/0.72 (step t498.t2.t7 (cl (= (= tptp.m (tptp.f tptp.n)) false) (not (not (= tptp.m (tptp.f tptp.n))))) :rule equiv2 :premises (t498.t2.t6))
% 0.55/0.72 (step t498.t2.t8 (cl (not (not (not (= tptp.m (tptp.f tptp.n))))) (= tptp.m (tptp.f tptp.n))) :rule not_not)
% 0.55/0.72 (step t498.t2.t9 (cl (= (= tptp.m (tptp.f tptp.n)) false) (= tptp.m (tptp.f tptp.n))) :rule resolution :premises (t498.t2.t7 t498.t2.t8))
% 0.55/0.72 (step t498.t2.t10 (cl (= (= tptp.m (tptp.f tptp.n)) false)) :rule resolution :premises (t498.t2.t9 t498.t2.a0))
% 0.55/0.72 (step t498.t2.t11 (cl (= (= tptp.k (tptp.f tptp.n)) false)) :rule trans :premises (t498.t2.t5 t498.t2.t10))
% 0.55/0.72 (step t498.t2.t12 (cl (not (= tptp.k (tptp.f tptp.n)))) :rule resolution :premises (t498.t2.t2 t498.t2.t11))
% 0.55/0.72 (step t498.t2 (cl (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n)))) :rule subproof :discharge (t498.t2.a0 t498.t2.a1))
% 0.55/0.72 (step t498.t3 (cl (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (= tptp.m (tptp.f tptp.n)))) :rule and_pos)
% 0.55/0.72 (step t498.t4 (cl (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t498.t5 (cl (not (= tptp.k (tptp.f tptp.n))) (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)))) :rule resolution :premises (t498.t2 t498.t3 t498.t4))
% 0.55/0.72 (step t498.t6 (cl (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (= tptp.k (tptp.f tptp.n)))) :rule reordering :premises (t498.t5))
% 0.55/0.72 (step t498.t7 (cl (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (= tptp.k (tptp.f tptp.n)))) :rule contraction :premises (t498.t6))
% 0.55/0.72 (step t498.t8 (cl (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) :rule resolution :premises (t498.t1 t498.t7))
% 0.55/0.72 (step t498.t9 (cl (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n)))) (not (not (= tptp.k (tptp.f tptp.n))))) :rule implies_neg2)
% 0.55/0.72 (step t498.t10 (cl (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n)))) (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n))))) :rule resolution :premises (t498.t8 t498.t9))
% 0.55/0.72 (step t498.t11 (cl (=> (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (= tptp.k (tptp.f tptp.n))))) :rule contraction :premises (t498.t10))
% 0.55/0.72 (step t498.t12 (cl (not (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) (not (= tptp.k (tptp.f tptp.n)))) :rule implies :premises (t498.t11))
% 0.55/0.72 (step t498.t13 (cl (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.m tptp.k))) :rule and_neg)
% 0.55/0.72 (step t498.t14 (cl (and (not (= tptp.m (tptp.f tptp.n))) (= tptp.m tptp.k))) :rule resolution :premises (t498.t13 t498.a1 t498.a0))
% 0.55/0.72 (step t498.t15 (cl (not (= tptp.k (tptp.f tptp.n)))) :rule resolution :premises (t498.t12 t498.t14))
% 0.55/0.72 (step t498 (cl (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) :rule subproof :discharge (t498.a0 t498.a1))
% 0.55/0.72 (step t499 (cl (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t500 (cl (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (= tptp.m (tptp.f tptp.n)))) :rule and_pos)
% 0.55/0.72 (step t501 (cl (not (= tptp.k (tptp.f tptp.n))) (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))))) :rule resolution :premises (t498 t499 t500))
% 0.55/0.72 (step t502 (cl (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (= tptp.k (tptp.f tptp.n)))) :rule reordering :premises (t501))
% 0.55/0.72 (step t503 (cl (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (= tptp.k (tptp.f tptp.n)))) :rule contraction :premises (t502))
% 0.55/0.72 (step t504 (cl (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) :rule resolution :premises (t497 t503))
% 0.55/0.72 (step t505 (cl (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (not (not (= tptp.k (tptp.f tptp.n))))) :rule implies_neg2)
% 0.55/0.72 (step t506 (cl (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n))))) :rule resolution :premises (t504 t505))
% 0.55/0.72 (step t507 (cl (=> (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n))))) :rule contraction :premises (t506))
% 0.55/0.72 (step t508 (cl (not (and (= tptp.m tptp.k) (not (= tptp.m (tptp.f tptp.n))))) (not (= tptp.k (tptp.f tptp.n)))) :rule implies :premises (t507))
% 0.55/0.72 (step t509 (cl (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) :rule resolution :premises (t496 t508))
% 0.55/0.72 (step t510 (cl (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (not (not (= tptp.m tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t511 (cl (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (not (not (not (= tptp.m (tptp.f tptp.n)))))) :rule or_neg)
% 0.55/0.72 (step t512 (cl (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (not (not (= tptp.k (tptp.f tptp.n))))) :rule or_neg)
% 0.55/0.72 (step t513 (cl (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n)))) (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n))))) :rule resolution :premises (t509 t510 t511 t512))
% 0.55/0.72 (step t514 (cl (or (not (= tptp.m tptp.k)) (not (not (= tptp.m (tptp.f tptp.n)))) (not (= tptp.k (tptp.f tptp.n))))) :rule contraction :premises (t513))
% 0.55/0.72 (step t515 (cl (or (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (not (= tptp.k (tptp.f tptp.n))))) :rule resolution :premises (t483 t495 t514))
% 0.55/0.72 (step t516 (cl (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (not (= tptp.k (tptp.f tptp.n)))) :rule or :premises (t515))
% 0.55/0.72 (step t517 (cl (not (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))) :rule or_pos)
% 0.55/0.72 (step t518 (cl (= tptp.n tptp.m) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))) (not (tptp.element (tptp.f tptp.n) tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (not (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule reordering :premises (t517))
% 0.55/0.72 (step t519 (cl (not (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))))) (not (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule equiv_pos2)
% 0.55/0.72 (step t520 (cl (= (tptp.element (tptp.f tptp.n) tptp.m) (tptp.element (tptp.f tptp.n) tptp.m))) :rule refl)
% 0.55/0.72 (step t521 (cl (= (= (tptp.f tptp.n) tptp.n) (= tptp.n (tptp.f tptp.n)))) :rule all_simplify)
% 0.55/0.72 (step t522 (cl (= (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)))) :rule refl)
% 0.55/0.72 (step t523 (cl (= (not (tptp.element tptp.n (tptp.f tptp.n))) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule refl)
% 0.55/0.72 (step t524 (cl (= (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule cong :premises (t487 t520 t353 t521 t522 t523))
% 0.55/0.72 (step t525 (cl (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))))) :rule cong :premises (t351 t524))
% 0.55/0.72 (step t526 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t527)
% 0.55/0.72 (assume t527.a0 (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))
% 0.55/0.72 (step t527.t1 (cl (or (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule forall_inst :args ((:= Y (tptp.f tptp.n)) (:= V1 tptp.n)))
% 0.55/0.72 (step t527.t2 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule or :premises (t527.t1))
% 0.55/0.72 (step t527.t3 (cl (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t527.t2 t527.a0))
% 0.55/0.72 (step t527 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule subproof :discharge (t527.a0))
% 0.55/0.72 (step t528 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t526 t527))
% 0.55/0.72 (step t529 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (not (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule implies_neg2)
% 0.55/0.72 (step t530 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule resolution :premises (t528 t529))
% 0.55/0.72 (step t531 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.m tptp.n) (= (tptp.f tptp.n) tptp.n) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule contraction :premises (t530))
% 0.55/0.72 (step t532 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n)))))) :rule resolution :premises (t519 t525 t531))
% 0.55/0.72 (step t533 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule implies :premises (t532))
% 0.55/0.72 (step t534 (cl (or (= tptp.m (tptp.f tptp.n)) (tptp.element (tptp.f tptp.n) tptp.m) (= tptp.n tptp.m) (= tptp.n (tptp.f tptp.n)) (not (tptp.element (tptp.f tptp.n) tptp.n)) (not (tptp.element tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t533 t303))
% 0.55/0.72 (step t535 (cl (not (= tptp.n tptp.m))) :rule not_symm :premises (a0))
% 0.55/0.72 (step t536 (cl (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)) :rule or_pos)
% 0.55/0.72 (step t537 (cl (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n) (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule reordering :premises (t536))
% 0.55/0.72 (step t538 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule equiv_pos2)
% 0.55/0.72 (step t539 (cl (= (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))) :rule refl)
% 0.55/0.72 (step t540 (cl (= (not (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m)))) :rule refl)
% 0.55/0.72 (step t541 (cl (= (tptp.element (tptp.f tptp.n) tptp.n) (tptp.element (tptp.f tptp.n) tptp.n))) :rule refl)
% 0.55/0.72 (step t542 (cl (= (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule cong :premises (t353 t540 t541))
% 0.55/0.72 (step t543 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))))) :rule cong :premises (t539 t542))
% 0.55/0.72 (step t544 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t545)
% 0.55/0.72 (assume t545.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))))
% 0.55/0.72 (step t545.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule forall_inst :args ((:= Y tptp.n)))
% 0.55/0.72 (step t545.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule or :premises (t545.t1))
% 0.55/0.72 (step t545.t3 (cl (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule resolution :premises (t545.t2 t545.a0))
% 0.55/0.72 (step t545 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule subproof :discharge (t545.a0))
% 0.55/0.72 (step t546 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule resolution :premises (t544 t545))
% 0.55/0.72 (step t547 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (not (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule implies_neg2)
% 0.55/0.72 (step t548 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule resolution :premises (t546 t547))
% 0.55/0.72 (step t549 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule contraction :premises (t548))
% 0.55/0.72 (step t550 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n)))) :rule resolution :premises (t538 t543 t549))
% 0.55/0.72 (step t551 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element (tptp.f Y) Y)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule implies :premises (t550))
% 0.55/0.72 (step t552 (cl (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element (tptp.f tptp.n) tptp.n))) :rule resolution :premises (t551 t186))
% 0.55/0.72 (step t553 (cl (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))) :rule or_pos)
% 0.55/0.72 (step t554 (cl (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)) (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule reordering :premises (t553))
% 0.55/0.72 (step t555 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule equiv_pos2)
% 0.55/0.72 (step t556 (cl (= (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))) :rule refl)
% 0.55/0.72 (step t557 (cl (= (tptp.element tptp.n (tptp.f tptp.n)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule refl)
% 0.55/0.72 (step t558 (cl (= (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule cong :premises (t353 t540 t557))
% 0.55/0.72 (step t559 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))))) :rule cong :premises (t556 t558))
% 0.55/0.72 (step t560 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t561)
% 0.55/0.72 (assume t561.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))))
% 0.55/0.72 (step t561.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule forall_inst :args ((:= Y tptp.n)))
% 0.55/0.72 (step t561.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule or :premises (t561.t1))
% 0.55/0.72 (step t561.t3 (cl (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule resolution :premises (t561.t2 t561.a0))
% 0.55/0.72 (step t561 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule subproof :discharge (t561.a0))
% 0.55/0.72 (step t562 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule resolution :premises (t560 t561))
% 0.55/0.72 (step t563 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (not (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule implies_neg2)
% 0.55/0.72 (step t564 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t562 t563))
% 0.55/0.72 (step t565 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule contraction :premises (t564))
% 0.55/0.72 (step t566 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t555 t559 t565))
% 0.55/0.72 (step t567 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (tptp.element Y (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule implies :premises (t566))
% 0.55/0.72 (step t568 (cl (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (tptp.element tptp.n (tptp.f tptp.n)))) :rule resolution :premises (t567 t199))
% 0.55/0.72 (step t569 (cl (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (= tptp.m tptp.k)) (not (= tptp.m tptp.k)) (= tptp.m (tptp.f tptp.n)) (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m))) :rule resolution :premises (t460 t468 t482 t516 t518 t534 t535 t537 t552 t535 t554 t568 t535))
% 0.55/0.72 (step t570 (cl (= tptp.m (tptp.f tptp.n)) (= tptp.n (tptp.f tptp.n)) (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.m))) :rule contraction :premises (t569))
% 0.55/0.72 (step t571 (cl (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))) :rule or_pos)
% 0.55/0.72 (step t572 (cl (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))) (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule reordering :premises (t571))
% 0.55/0.72 (step t573 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule equiv_pos2)
% 0.55/0.72 (step t574 (cl (= (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))))) :rule refl)
% 0.55/0.72 (step t575 (cl (= (not (= tptp.n (tptp.f tptp.n))) (not (= tptp.n (tptp.f tptp.n))))) :rule refl)
% 0.55/0.72 (step t576 (cl (= (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule cong :premises (t353 t540 t575))
% 0.55/0.72 (step t577 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))))) :rule cong :premises (t574 t576))
% 0.55/0.72 (step t578 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t579)
% 0.55/0.72 (assume t579.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))))
% 0.55/0.72 (step t579.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule forall_inst :args ((:= Y tptp.n)))
% 0.55/0.72 (step t579.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule or :premises (t579.t1))
% 0.55/0.72 (step t579.t3 (cl (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t579.t2 t579.a0))
% 0.55/0.72 (step t579 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule subproof :discharge (t579.a0))
% 0.55/0.72 (step t580 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t578 t579))
% 0.55/0.72 (step t581 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (not (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule implies_neg2)
% 0.55/0.72 (step t582 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule resolution :premises (t580 t581))
% 0.55/0.72 (step t583 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule contraction :premises (t582))
% 0.55/0.72 (step t584 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n)))))) :rule resolution :premises (t573 t577 t583))
% 0.55/0.72 (step t585 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= Y (tptp.f Y)))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule implies :premises (t584))
% 0.55/0.72 (step t586 (cl (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.n (tptp.f tptp.n))))) :rule resolution :premises (t585 t212))
% 0.55/0.72 (step t587 (cl (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))) :rule or_pos)
% 0.55/0.72 (step t588 (cl (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))) (not (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule reordering :premises (t587))
% 0.55/0.72 (step t589 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule equiv_pos2)
% 0.55/0.72 (step t590 (cl (= (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))))) :rule refl)
% 0.55/0.72 (step t591 (cl (= (not (= tptp.m (tptp.f tptp.n))) (not (= tptp.m (tptp.f tptp.n))))) :rule refl)
% 0.55/0.72 (step t592 (cl (= (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule cong :premises (t353 t540 t591))
% 0.55/0.72 (step t593 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))))) :rule cong :premises (t590 t592))
% 0.55/0.72 (step t594 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t595)
% 0.55/0.72 (assume t595.a0 (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))))
% 0.55/0.72 (step t595.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule forall_inst :args ((:= Y tptp.n)))
% 0.55/0.72 (step t595.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule or :premises (t595.t1))
% 0.55/0.72 (step t595.t3 (cl (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule resolution :premises (t595.t2 t595.a0))
% 0.55/0.72 (step t595 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule subproof :discharge (t595.a0))
% 0.55/0.72 (step t596 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule resolution :premises (t594 t595))
% 0.55/0.72 (step t597 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (not (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule implies_neg2)
% 0.55/0.72 (step t598 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule resolution :premises (t596 t597))
% 0.55/0.72 (step t599 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.m tptp.n) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule contraction :premises (t598))
% 0.55/0.72 (step t600 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n)))))) :rule resolution :premises (t589 t593 t599))
% 0.55/0.72 (step t601 (cl (not (forall ((Y $$unsorted)) (or (= tptp.m Y) (not (tptp.element Y tptp.m)) (not (= tptp.m (tptp.f Y)))))) (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule implies :premises (t600))
% 0.55/0.72 (step t602 (cl (or (= tptp.n tptp.m) (not (tptp.element tptp.n tptp.m)) (not (= tptp.m (tptp.f tptp.n))))) :rule resolution :premises (t601 t225))
% 0.55/0.72 (step t603 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m))) :rule resolution :premises (t570 t572 t586 t535 t588 t602 t535))
% 0.55/0.72 (step t604 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.m))) :rule contraction :premises (t603))
% 0.55/0.72 (step t605 (cl (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k))) :rule and_neg)
% 0.55/0.72 (step t606 (cl (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t607)
% 0.55/0.72 (assume t607.a0 (= tptp.m tptp.k))
% 0.55/0.72 (assume t607.a1 (tptp.element tptp.n tptp.k))
% 0.55/0.72 (step t607.t1 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m)) (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t607.t2)
% 0.55/0.72 (assume t607.t2.a0 (tptp.element tptp.n tptp.k))
% 0.55/0.72 (assume t607.t2.a1 (= tptp.m tptp.k))
% 0.55/0.72 (step t607.t2.t1 (cl (= (= (tptp.element tptp.n tptp.m) true) (tptp.element tptp.n tptp.m))) :rule equiv_simplify)
% 0.55/0.72 (step t607.t2.t2 (cl (not (= (tptp.element tptp.n tptp.m) true)) (tptp.element tptp.n tptp.m)) :rule equiv1 :premises (t607.t2.t1))
% 0.55/0.72 (step t607.t2.t3 (cl (= tptp.n tptp.n)) :rule refl)
% 0.55/0.72 (step t607.t2.t4 (cl (= tptp.k tptp.m)) :rule symm :premises (t607.t2.a1))
% 0.55/0.72 (step t607.t2.t5 (cl (= tptp.m tptp.k)) :rule symm :premises (t607.t2.t4))
% 0.55/0.72 (step t607.t2.t6 (cl (= (tptp.element tptp.n tptp.m) (tptp.element tptp.n tptp.k))) :rule cong :premises (t607.t2.t3 t607.t2.t5))
% 0.55/0.72 (step t607.t2.t7 (cl (= (= (tptp.element tptp.n tptp.k) true) (tptp.element tptp.n tptp.k))) :rule equiv_simplify)
% 0.55/0.72 (step t607.t2.t8 (cl (= (tptp.element tptp.n tptp.k) true) (not (tptp.element tptp.n tptp.k))) :rule equiv2 :premises (t607.t2.t7))
% 0.55/0.72 (step t607.t2.t9 (cl (= (tptp.element tptp.n tptp.k) true)) :rule resolution :premises (t607.t2.t8 t607.t2.a0))
% 0.55/0.72 (step t607.t2.t10 (cl (= (tptp.element tptp.n tptp.m) true)) :rule trans :premises (t607.t2.t6 t607.t2.t9))
% 0.55/0.72 (step t607.t2.t11 (cl (tptp.element tptp.n tptp.m)) :rule resolution :premises (t607.t2.t2 t607.t2.t10))
% 0.55/0.72 (step t607.t2 (cl (not (tptp.element tptp.n tptp.k)) (not (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m)) :rule subproof :discharge (t607.t2.a0 t607.t2.a1))
% 0.55/0.72 (step t607.t3 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (tptp.element tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t607.t4 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t607.t5 (cl (tptp.element tptp.n tptp.m) (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)))) :rule resolution :premises (t607.t2 t607.t3 t607.t4))
% 0.55/0.72 (step t607.t6 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (tptp.element tptp.n tptp.m)) :rule reordering :premises (t607.t5))
% 0.55/0.72 (step t607.t7 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (tptp.element tptp.n tptp.m)) :rule contraction :premises (t607.t6))
% 0.55/0.72 (step t607.t8 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m)) (tptp.element tptp.n tptp.m)) :rule resolution :premises (t607.t1 t607.t7))
% 0.55/0.72 (step t607.t9 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m))) :rule implies_neg2)
% 0.55/0.72 (step t607.t10 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m)) (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m))) :rule resolution :premises (t607.t8 t607.t9))
% 0.55/0.72 (step t607.t11 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (tptp.element tptp.n tptp.m))) :rule contraction :premises (t607.t10))
% 0.55/0.72 (step t607.t12 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) (tptp.element tptp.n tptp.m)) :rule implies :premises (t607.t11))
% 0.55/0.72 (step t607.t13 (cl (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k)) (not (= tptp.m tptp.k))) :rule and_neg)
% 0.55/0.72 (step t607.t14 (cl (and (tptp.element tptp.n tptp.k) (= tptp.m tptp.k))) :rule resolution :premises (t607.t13 t607.a1 t607.a0))
% 0.55/0.72 (step t607.t15 (cl (tptp.element tptp.n tptp.m)) :rule resolution :premises (t607.t12 t607.t14))
% 0.55/0.72 (step t607 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) :rule subproof :discharge (t607.a0 t607.a1))
% 0.55/0.72 (step t608 (cl (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t609 (cl (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t610 (cl (tptp.element tptp.n tptp.m) (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)))) :rule resolution :premises (t607 t608 t609))
% 0.55/0.72 (step t611 (cl (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.m)) :rule reordering :premises (t610))
% 0.55/0.72 (step t612 (cl (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.m)) :rule contraction :premises (t611))
% 0.55/0.72 (step t613 (cl (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) (tptp.element tptp.n tptp.m)) :rule resolution :premises (t606 t612))
% 0.55/0.72 (step t614 (cl (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) (not (tptp.element tptp.n tptp.m))) :rule implies_neg2)
% 0.55/0.72 (step t615 (cl (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m))) :rule resolution :premises (t613 t614))
% 0.55/0.72 (step t616 (cl (=> (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m))) :rule contraction :premises (t615))
% 0.55/0.72 (step t617 (cl (not (and (= tptp.m tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.m)) :rule implies :premises (t616))
% 0.55/0.72 (step t618 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.m)) :rule resolution :premises (t605 t617))
% 0.55/0.72 (step t619 (cl (not (= tptp.m tptp.k)) (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k))) :rule resolution :premises (t604 t618))
% 0.55/0.72 (step t620 (cl (not (= tptp.m tptp.k)) (not (tptp.element tptp.n tptp.k))) :rule contraction :premises (t619))
% 0.55/0.72 (step t621 (cl (= tptp.n tptp.k) (= tptp.n tptp.k)) :rule resolution :premises (t458 t620 t383))
% 0.55/0.72 (step t622 (cl (= tptp.n tptp.k)) :rule contraction :premises (t621))
% 0.55/0.72 (step t623 (cl (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))) :rule or_pos)
% 0.55/0.72 (step t624 (cl (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))))) :rule reordering :premises (t623))
% 0.55/0.72 (step t625 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t626)
% 0.55/0.72 (assume t626.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))))
% 0.55/0.72 (step t626.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))))) :rule forall_inst :args ((:= Y tptp.j)))
% 0.55/0.72 (step t626.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule or :premises (t626.t1))
% 0.55/0.72 (step t626.t3 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule resolution :premises (t626.t2 t626.a0))
% 0.55/0.72 (step t626 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule subproof :discharge (t626.a0))
% 0.55/0.72 (step t627 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule resolution :premises (t625 t626))
% 0.55/0.72 (step t628 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))))) :rule implies_neg2)
% 0.55/0.72 (step t629 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))))) :rule resolution :premises (t627 t628))
% 0.55/0.72 (step t630 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j)))))) :rule contraction :premises (t629))
% 0.55/0.72 (step t631 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule implies :premises (t630))
% 0.55/0.72 (step t632 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) tptp.n)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) tptp.n))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t633 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t633.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t633.t2 (cl (= (= Y tptp.n) (= tptp.n Y))) :rule all_simplify)
% 0.55/0.72 (step t633.t3 (cl (= (tptp.element Y tptp.n) (tptp.element Y tptp.n))) :rule refl)
% 0.55/0.72 (step t633.t4 (cl (= (= (tptp.g Y) tptp.n) (= tptp.n (tptp.g Y)))) :rule all_simplify)
% 0.55/0.72 (step t633.t5 (cl (= (not (= (tptp.g Y) tptp.n)) (not (= tptp.n (tptp.g Y))))) :rule cong :premises (t633.t4))
% 0.55/0.72 (step t633.t6 (cl (= (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) tptp.n))) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) :rule cong :premises (t633.t2 t633.t3 t633.t5))
% 0.55/0.72 (step t633 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.n) (tptp.element Y tptp.n) (not (= (tptp.g Y) tptp.n)))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y))))))) :rule bind)
% 0.55/0.72 (step t634 (cl (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= tptp.n (tptp.g Y)))))) :rule resolution :premises (t632 t633 a8))
% 0.55/0.72 (step t635 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.n (tptp.g tptp.j))))) :rule resolution :premises (t631 t634))
% 0.55/0.72 (step t636 (cl (not (= (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (or (not (= tptp.n tptp.k)) (tptp.element tptp.j tptp.k) (not (tptp.element tptp.j tptp.n))))) (not (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n)))) (or (not (= tptp.n tptp.k)) (tptp.element tptp.j tptp.k) (not (tptp.element tptp.j tptp.n)))) :rule equiv_pos2)
% 0.55/0.72 (step t637 (cl (= (= (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k)) true) (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t638 (cl (not (= (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k)) true)) (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k))) :rule equiv1 :premises (t637))
% 0.55/0.72 (step t639 (cl (= (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k)) (= (tptp.element tptp.j tptp.k) (not (not (tptp.element tptp.j tptp.k)))))) :rule all_simplify)
% 0.55/0.72 (step t640 (cl (= (tptp.element tptp.j tptp.k) (tptp.element tptp.j tptp.k))) :rule refl)
% 0.55/0.72 (step t641 (cl (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k))) :rule all_simplify)
% 0.55/0.72 (step t642 (cl (= (= (tptp.element tptp.j tptp.k) (not (not (tptp.element tptp.j tptp.k)))) (= (tptp.element tptp.j tptp.k) (tptp.element tptp.j tptp.k)))) :rule cong :premises (t640 t641))
% 0.55/0.72 (step t643 (cl (= (= (tptp.element tptp.j tptp.k) (tptp.element tptp.j tptp.k)) true)) :rule all_simplify)
% 0.55/0.72 (step t644 (cl (= (= (tptp.element tptp.j tptp.k) (not (not (tptp.element tptp.j tptp.k)))) true)) :rule trans :premises (t642 t643))
% 0.55/0.72 (step t645 (cl (= (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k)) true)) :rule trans :premises (t639 t644))
% 0.55/0.72 (step t646 (cl (= (not (not (tptp.element tptp.j tptp.k))) (tptp.element tptp.j tptp.k))) :rule resolution :premises (t638 t645))
% 0.55/0.72 (step t647 (cl (= (not (tptp.element tptp.j tptp.n)) (not (tptp.element tptp.j tptp.n)))) :rule refl)
% 0.55/0.72 (step t648 (cl (= (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (or (not (= tptp.n tptp.k)) (tptp.element tptp.j tptp.k) (not (tptp.element tptp.j tptp.n))))) :rule cong :premises (t2 t646 t647))
% 0.55/0.72 (step t649 (cl (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k)))) :rule and_neg)
% 0.55/0.72 (step t650 (cl (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t651)
% 0.55/0.72 (assume t651.a0 (= tptp.n tptp.k))
% 0.55/0.72 (assume t651.a1 (not (tptp.element tptp.j tptp.k)))
% 0.55/0.72 (step t651.t1 (cl (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n))) (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t651.t2)
% 0.55/0.72 (assume t651.t2.a0 (not (tptp.element tptp.j tptp.k)))
% 0.55/0.72 (assume t651.t2.a1 (= tptp.n tptp.k))
% 0.55/0.72 (step t651.t2.t1 (cl (= (= (tptp.element tptp.j tptp.n) false) (not (tptp.element tptp.j tptp.n)))) :rule equiv_simplify)
% 0.55/0.72 (step t651.t2.t2 (cl (not (= (tptp.element tptp.j tptp.n) false)) (not (tptp.element tptp.j tptp.n))) :rule equiv1 :premises (t651.t2.t1))
% 0.55/0.72 (step t651.t2.t3 (cl (= tptp.j tptp.j)) :rule refl)
% 0.55/0.72 (step t651.t2.t4 (cl (= tptp.k tptp.n)) :rule symm :premises (t651.t2.a1))
% 0.55/0.72 (step t651.t2.t5 (cl (= tptp.n tptp.k)) :rule symm :premises (t651.t2.t4))
% 0.55/0.72 (step t651.t2.t6 (cl (= (tptp.element tptp.j tptp.n) (tptp.element tptp.j tptp.k))) :rule cong :premises (t651.t2.t3 t651.t2.t5))
% 0.55/0.72 (step t651.t2.t7 (cl (= (= (tptp.element tptp.j tptp.k) false) (not (tptp.element tptp.j tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t651.t2.t8 (cl (= (tptp.element tptp.j tptp.k) false) (not (not (tptp.element tptp.j tptp.k)))) :rule equiv2 :premises (t651.t2.t7))
% 0.55/0.72 (step t651.t2.t9 (cl (not (not (not (tptp.element tptp.j tptp.k)))) (tptp.element tptp.j tptp.k)) :rule not_not)
% 0.55/0.72 (step t651.t2.t10 (cl (= (tptp.element tptp.j tptp.k) false) (tptp.element tptp.j tptp.k)) :rule resolution :premises (t651.t2.t8 t651.t2.t9))
% 0.55/0.72 (step t651.t2.t11 (cl (= (tptp.element tptp.j tptp.k) false)) :rule resolution :premises (t651.t2.t10 t651.t2.a0))
% 0.55/0.72 (step t651.t2.t12 (cl (= (tptp.element tptp.j tptp.n) false)) :rule trans :premises (t651.t2.t6 t651.t2.t11))
% 0.55/0.72 (step t651.t2.t13 (cl (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t651.t2.t2 t651.t2.t12))
% 0.55/0.72 (step t651.t2 (cl (not (not (tptp.element tptp.j tptp.k))) (not (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n))) :rule subproof :discharge (t651.t2.a0 t651.t2.a1))
% 0.55/0.72 (step t651.t3 (cl (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (tptp.element tptp.j tptp.k))) :rule and_pos)
% 0.55/0.72 (step t651.t4 (cl (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t651.t5 (cl (not (tptp.element tptp.j tptp.n)) (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)))) :rule resolution :premises (t651.t2 t651.t3 t651.t4))
% 0.55/0.72 (step t651.t6 (cl (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (tptp.element tptp.j tptp.n))) :rule reordering :premises (t651.t5))
% 0.55/0.72 (step t651.t7 (cl (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (tptp.element tptp.j tptp.n))) :rule contraction :premises (t651.t6))
% 0.55/0.72 (step t651.t8 (cl (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n))) (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t651.t1 t651.t7))
% 0.55/0.72 (step t651.t9 (cl (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n))) (not (not (tptp.element tptp.j tptp.n)))) :rule implies_neg2)
% 0.55/0.72 (step t651.t10 (cl (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n))) (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n)))) :rule resolution :premises (t651.t8 t651.t9))
% 0.55/0.72 (step t651.t11 (cl (=> (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (tptp.element tptp.j tptp.n)))) :rule contraction :premises (t651.t10))
% 0.55/0.72 (step t651.t12 (cl (not (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) (not (tptp.element tptp.j tptp.n))) :rule implies :premises (t651.t11))
% 0.55/0.72 (step t651.t13 (cl (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (= tptp.n tptp.k))) :rule and_neg)
% 0.55/0.72 (step t651.t14 (cl (and (not (tptp.element tptp.j tptp.k)) (= tptp.n tptp.k))) :rule resolution :premises (t651.t13 t651.a1 t651.a0))
% 0.55/0.72 (step t651.t15 (cl (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t651.t12 t651.t14))
% 0.55/0.72 (step t651 (cl (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) :rule subproof :discharge (t651.a0 t651.a1))
% 0.55/0.72 (step t652 (cl (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t653 (cl (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (tptp.element tptp.j tptp.k))) :rule and_pos)
% 0.55/0.72 (step t654 (cl (not (tptp.element tptp.j tptp.n)) (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))))) :rule resolution :premises (t651 t652 t653))
% 0.55/0.72 (step t655 (cl (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (tptp.element tptp.j tptp.n))) :rule reordering :premises (t654))
% 0.55/0.72 (step t656 (cl (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (tptp.element tptp.j tptp.n))) :rule contraction :premises (t655))
% 0.55/0.72 (step t657 (cl (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t650 t656))
% 0.55/0.72 (step t658 (cl (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (not (not (tptp.element tptp.j tptp.n)))) :rule implies_neg2)
% 0.55/0.72 (step t659 (cl (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n)))) :rule resolution :premises (t657 t658))
% 0.55/0.72 (step t660 (cl (=> (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n)))) :rule contraction :premises (t659))
% 0.55/0.72 (step t661 (cl (not (and (= tptp.n tptp.k) (not (tptp.element tptp.j tptp.k)))) (not (tptp.element tptp.j tptp.n))) :rule implies :premises (t660))
% 0.55/0.72 (step t662 (cl (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t649 t661))
% 0.55/0.72 (step t663 (cl (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t664 (cl (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (not (not (not (tptp.element tptp.j tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t665 (cl (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (not (not (tptp.element tptp.j tptp.n)))) :rule or_neg)
% 0.55/0.72 (step t666 (cl (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n))) (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n)))) :rule resolution :premises (t662 t663 t664 t665))
% 0.55/0.72 (step t667 (cl (or (not (= tptp.n tptp.k)) (not (not (tptp.element tptp.j tptp.k))) (not (tptp.element tptp.j tptp.n)))) :rule contraction :premises (t666))
% 0.55/0.72 (step t668 (cl (or (not (= tptp.n tptp.k)) (tptp.element tptp.j tptp.k) (not (tptp.element tptp.j tptp.n)))) :rule resolution :premises (t636 t648 t667))
% 0.55/0.72 (step t669 (cl (not (= tptp.n tptp.k)) (tptp.element tptp.j tptp.k) (not (tptp.element tptp.j tptp.n))) :rule or :premises (t668))
% 0.55/0.72 (step t670 (cl (not (= (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (tptp.element tptp.k tptp.m)))) (not (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m))))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (tptp.element tptp.k tptp.m))) :rule equiv_pos2)
% 0.55/0.72 (step t671 (cl (= (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.k tptp.j)))) :rule refl)
% 0.55/0.72 (step t672 (cl (= (not (= tptp.m tptp.j)) (not (= tptp.m tptp.j)))) :rule refl)
% 0.55/0.72 (step t673 (cl (= (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (tptp.element tptp.k tptp.m)))) :rule cong :premises (t671 t2 t672 t242))
% 0.55/0.72 (step t674 (cl (not (= (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))))) (not (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))))) :rule equiv_pos2)
% 0.55/0.72 (step t675 (cl (= (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))))) :rule refl)
% 0.55/0.72 (step t676 (cl (= (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))))) :rule equiv_simplify)
% 0.55/0.72 (step t677 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))))) :rule equiv2 :premises (t676))
% 0.55/0.72 (step t678 (cl (not (not (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule not_not)
% 0.55/0.72 (step t679 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule resolution :premises (t677 t678))
% 0.55/0.72 (step t680 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t681)
% 0.55/0.72 (assume t681.a0 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (assume t681.a1 (= tptp.n tptp.k))
% 0.55/0.72 (assume t681.a2 (= tptp.m tptp.j))
% 0.55/0.72 (assume t681.a3 (tptp.element tptp.k tptp.j))
% 0.55/0.72 (step t681.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.55/0.72 (step t681.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.55/0.72 (step t681.t3 (cl (= (= (tptp.element tptp.k tptp.j) true) (tptp.element tptp.k tptp.j))) :rule equiv_simplify)
% 0.55/0.72 (step t681.t4 (cl (= (tptp.element tptp.k tptp.j) true) (not (tptp.element tptp.k tptp.j))) :rule equiv2 :premises (t681.t3))
% 0.55/0.72 (step t681.t5 (cl (= (tptp.element tptp.k tptp.j) true)) :rule resolution :premises (t681.t4 t681.a3))
% 0.55/0.72 (step t681.t6 (cl (= true (tptp.element tptp.k tptp.j))) :rule symm :premises (t681.t5))
% 0.55/0.72 (step t681.t7 (cl (= tptp.k tptp.n)) :rule symm :premises (t681.a1))
% 0.55/0.72 (step t681.t8 (cl (= tptp.j tptp.j)) :rule refl)
% 0.55/0.72 (step t681.t9 (cl (= (tptp.element tptp.k tptp.j) (tptp.element tptp.n tptp.j))) :rule cong :premises (t681.t7 t681.t8))
% 0.55/0.72 (step t681.t10 (cl (= tptp.n tptp.k)) :rule symm :premises (t681.t7))
% 0.55/0.72 (step t681.t11 (cl (= tptp.j tptp.m)) :rule symm :premises (t681.a2))
% 0.55/0.72 (step t681.t12 (cl (= (tptp.element tptp.n tptp.j) (tptp.element tptp.k tptp.m))) :rule cong :premises (t681.t10 t681.t11))
% 0.55/0.72 (step t681.t13 (cl (= (= (tptp.element tptp.k tptp.m) false) (not (tptp.element tptp.k tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t681.t14 (cl (= (tptp.element tptp.k tptp.m) false) (not (not (tptp.element tptp.k tptp.m)))) :rule equiv2 :premises (t681.t13))
% 0.55/0.72 (step t681.t15 (cl (not (not (not (tptp.element tptp.k tptp.m)))) (tptp.element tptp.k tptp.m)) :rule not_not)
% 0.55/0.72 (step t681.t16 (cl (= (tptp.element tptp.k tptp.m) false) (tptp.element tptp.k tptp.m)) :rule resolution :premises (t681.t14 t681.t15))
% 0.55/0.72 (step t681.t17 (cl (= (tptp.element tptp.k tptp.m) false)) :rule resolution :premises (t681.t16 t681.a0))
% 0.55/0.72 (step t681.t18 (cl (= true false)) :rule trans :premises (t681.t6 t681.t9 t681.t12 t681.t17))
% 0.55/0.72 (step t681.t19 (cl false) :rule resolution :premises (t681.t1 t681.t2 t681.t18))
% 0.55/0.72 (step t681 (cl (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (tptp.element tptp.k tptp.j)) false) :rule subproof :discharge (t681.a0 t681.a1 t681.a2 t681.a3))
% 0.55/0.72 (step t682 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t683 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t684 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (= tptp.m tptp.j)) :rule and_pos)
% 0.55/0.72 (step t685 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (tptp.element tptp.k tptp.j)) :rule and_pos)
% 0.55/0.72 (step t686 (cl false (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule resolution :premises (t681 t682 t683 t684 t685))
% 0.55/0.72 (step t687 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) false) :rule reordering :premises (t686))
% 0.55/0.72 (step t688 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) false) :rule contraction :premises (t687))
% 0.55/0.72 (step t689 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) false) :rule resolution :premises (t680 t688))
% 0.55/0.72 (step t690 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t691 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false)) :rule resolution :premises (t689 t690))
% 0.55/0.72 (step t692 (cl (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false)) :rule contraction :premises (t691))
% 0.55/0.72 (step t693 (cl (= (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))))) :rule implies_simplify)
% 0.55/0.72 (step t694 (cl (not (=> (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false)) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule equiv1 :premises (t693))
% 0.55/0.72 (step t695 (cl (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule resolution :premises (t692 t694))
% 0.55/0.72 (step t696 (cl (= (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) false)) :rule resolution :premises (t679 t695))
% 0.55/0.72 (step t697 (cl (= (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) false))) :rule cong :premises (t675 t696))
% 0.55/0.72 (step t698 (cl (= (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) false) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))))) :rule all_simplify)
% 0.55/0.72 (step t699 (cl (= (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))))) :rule trans :premises (t697 t698))
% 0.55/0.72 (step t700 (cl (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t701)
% 0.55/0.72 (assume t701.a0 (tptp.element tptp.k tptp.j))
% 0.55/0.72 (assume t701.a1 (= tptp.n tptp.k))
% 0.55/0.72 (assume t701.a2 (= tptp.m tptp.j))
% 0.55/0.72 (assume t701.a3 (not (tptp.element tptp.k tptp.m)))
% 0.55/0.72 (step t701.t1 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) (not (not (tptp.element tptp.k tptp.m))) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (tptp.element tptp.k tptp.j))) :rule and_neg)
% 0.55/0.72 (step t701.t2 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule resolution :premises (t701.t1 t701.a3 t701.a1 t701.a2 t701.a0))
% 0.55/0.72 (step t701 (cl (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule subproof :discharge (t701.a0 t701.a1 t701.a2 t701.a3))
% 0.55/0.72 (step t702 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (tptp.element tptp.k tptp.j)) :rule and_pos)
% 0.55/0.72 (step t703 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t704 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (= tptp.m tptp.j)) :rule and_pos)
% 0.55/0.72 (step t705 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (tptp.element tptp.k tptp.m))) :rule and_pos)
% 0.55/0.72 (step t706 (cl (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t701 t702 t703 t704 t705))
% 0.55/0.72 (step t707 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule reordering :premises (t706))
% 0.55/0.72 (step t708 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m)))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule contraction :premises (t707))
% 0.55/0.72 (step t709 (cl (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) :rule resolution :premises (t700 t708))
% 0.55/0.72 (step t710 (cl (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (not (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t711 (cl (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j))) (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule resolution :premises (t709 t710))
% 0.55/0.72 (step t712 (cl (=> (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))) (and (not (tptp.element tptp.k tptp.m)) (= tptp.n tptp.k) (= tptp.m tptp.j) (tptp.element tptp.k tptp.j)))) :rule contraction :premises (t711))
% 0.55/0.72 (step t713 (cl (not (and (tptp.element tptp.k tptp.j) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t674 t699 t712))
% 0.55/0.72 (step t714 (cl (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) :rule not_and :premises (t713))
% 0.55/0.72 (step t715 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (tptp.element tptp.k tptp.j)))) :rule or_neg)
% 0.55/0.72 (step t716 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t717 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (= tptp.m tptp.j)))) :rule or_neg)
% 0.55/0.72 (step t718 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (not (not (not (tptp.element tptp.k tptp.m))))) :rule or_neg)
% 0.55/0.72 (step t719 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m)))) (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m))))) :rule resolution :premises (t714 t715 t716 t717 t718))
% 0.55/0.72 (step t720 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (tptp.element tptp.k tptp.m))))) :rule contraction :premises (t719))
% 0.55/0.72 (step t721 (cl (or (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (tptp.element tptp.k tptp.m))) :rule resolution :premises (t670 t673 t720))
% 0.55/0.72 (step t722 (cl (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (tptp.element tptp.k tptp.m)) :rule or :premises (t721))
% 0.55/0.72 (step t723 (cl (not (tptp.element tptp.k tptp.j)) (not (= tptp.n tptp.k)) (tptp.element tptp.k tptp.m) (not (= tptp.m tptp.j))) :rule reordering :premises (t722))
% 0.55/0.72 (step t724 (cl (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))) :rule or_pos)
% 0.55/0.72 (step t725 (cl (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.j)) (= tptp.m tptp.j) (not (tptp.element tptp.j tptp.k)) (tptp.element tptp.k tptp.m) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule reordering :premises (t724))
% 0.55/0.72 (step t726 (cl (not (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))))) (not (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t727 (cl (= (= tptp.m tptp.j) (= tptp.m tptp.j))) :rule refl)
% 0.55/0.72 (step t728 (cl (= (= tptp.k tptp.j) (= tptp.j tptp.k))) :rule all_simplify)
% 0.55/0.72 (step t729 (cl (= (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.k tptp.j)))) :rule refl)
% 0.55/0.72 (step t730 (cl (= (not (tptp.element tptp.j tptp.k)) (not (tptp.element tptp.j tptp.k)))) :rule refl)
% 0.55/0.72 (step t731 (cl (= (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule cong :premises (t352 t236 t727 t728 t729 t730))
% 0.55/0.72 (step t732 (cl (= (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))))) :rule cong :premises (t351 t731))
% 0.55/0.72 (step t733 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t734)
% 0.55/0.72 (assume t734.a0 (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))))
% 0.55/0.72 (step t734.t1 (cl (or (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule forall_inst :args ((:= Y tptp.k) (:= V1 tptp.j)))
% 0.55/0.72 (step t734.t2 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule or :premises (t734.t1))
% 0.55/0.72 (step t734.t3 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule resolution :premises (t734.t2 t734.a0))
% 0.55/0.72 (step t734 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule subproof :discharge (t734.a0))
% 0.55/0.72 (step t735 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule resolution :premises (t733 t734))
% 0.55/0.72 (step t736 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (not (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t737 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule resolution :premises (t735 t736))
% 0.55/0.72 (step t738 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.k tptp.j) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule contraction :premises (t737))
% 0.55/0.72 (step t739 (cl (=> (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y)))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k))))) :rule resolution :premises (t726 t732 t738))
% 0.55/0.72 (step t740 (cl (not (forall ((Y $$unsorted) (V1 $$unsorted)) (or (= tptp.m Y) (tptp.element Y tptp.m) (= tptp.m V1) (= Y V1) (not (tptp.element Y V1)) (not (tptp.element V1 Y))))) (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule implies :premises (t739))
% 0.55/0.72 (step t741 (cl (or (= tptp.m tptp.k) (tptp.element tptp.k tptp.m) (= tptp.m tptp.j) (= tptp.j tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)))) :rule resolution :premises (t740 t303))
% 0.55/0.72 (step t742 (cl (not (tptp.element tptp.k tptp.j)) (tptp.element tptp.k tptp.m) (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.k tptp.j)) (not (tptp.element tptp.j tptp.k)) (tptp.element tptp.k tptp.m) (tptp.element tptp.k tptp.m) (= tptp.m tptp.k)) :rule resolution :premises (t723 t725 t741 t439 t456))
% 0.55/0.72 (step t743 (cl (not (tptp.element tptp.k tptp.j)) (tptp.element tptp.k tptp.m) (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.j tptp.k))) :rule contraction :premises (t742))
% 0.55/0.72 (step t744 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j))) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)))) (not (forall ((Y $$unsorted)) (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j)))) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t745 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t745.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t745.t2 (cl (= (= Y tptp.j) (= tptp.j Y))) :rule all_simplify)
% 0.55/0.72 (step t745.t3 (cl (= (= Y tptp.k) (= tptp.k Y))) :rule all_simplify)
% 0.55/0.72 (step t745.t4 (cl (= (not (= Y tptp.k)) (not (= tptp.k Y)))) :rule cong :premises (t745.t3))
% 0.55/0.72 (step t745.t5 (cl (= (tptp.element Y tptp.j) (tptp.element Y tptp.j))) :rule refl)
% 0.55/0.72 (step t745.t6 (cl (= (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j)) (or (= tptp.j Y) (not (= tptp.k Y)) (tptp.element Y tptp.j)))) :rule cong :premises (t745.t2 t745.t4 t745.t5))
% 0.55/0.72 (step t745 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (not (= tptp.k Y)) (tptp.element Y tptp.j))))) :rule bind)
% 0.55/0.72 (step t746 (cl (= (forall ((Y $$unsorted)) (or (= tptp.j Y) (not (= tptp.k Y)) (tptp.element Y tptp.j))) (or (= tptp.j tptp.k) (not (= tptp.k tptp.k)) (tptp.element tptp.k tptp.j)))) :rule all_simplify)
% 0.55/0.72 (step t747 (cl (= (= tptp.k tptp.k) true)) :rule all_simplify)
% 0.55/0.72 (step t748 (cl (= (not (= tptp.k tptp.k)) (not true))) :rule cong :premises (t747))
% 0.55/0.72 (step t749 (cl (= (not (= tptp.k tptp.k)) false)) :rule trans :premises (t748 t373))
% 0.55/0.72 (step t750 (cl (= (tptp.element tptp.k tptp.j) (tptp.element tptp.k tptp.j))) :rule refl)
% 0.55/0.72 (step t751 (cl (= (or (= tptp.j tptp.k) (not (= tptp.k tptp.k)) (tptp.element tptp.k tptp.j)) (or (= tptp.j tptp.k) false (tptp.element tptp.k tptp.j)))) :rule cong :premises (t6 t749 t750))
% 0.55/0.72 (step t752 (cl (= (or (= tptp.j tptp.k) false (tptp.element tptp.k tptp.j)) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)))) :rule all_simplify)
% 0.55/0.72 (step t753 (cl (= (or (= tptp.j tptp.k) (not (= tptp.k tptp.k)) (tptp.element tptp.k tptp.j)) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)))) :rule trans :premises (t751 t752))
% 0.55/0.72 (step t754 (cl (= (forall ((Y $$unsorted)) (or (= tptp.j Y) (not (= tptp.k Y)) (tptp.element Y tptp.j))) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)))) :rule trans :premises (t746 t753))
% 0.55/0.72 (step t755 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.j) (not (= Y tptp.k)) (tptp.element Y tptp.j))) (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)))) :rule trans :premises (t745 t754))
% 0.55/0.72 (step t756 (cl (or (= tptp.j tptp.k) (tptp.element tptp.k tptp.j))) :rule resolution :premises (t744 t755 a1))
% 0.55/0.72 (step t757 (cl (= tptp.j tptp.k) (tptp.element tptp.k tptp.j)) :rule or :premises (t756))
% 0.55/0.72 (step t758 (cl (tptp.element tptp.k tptp.m) (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.j tptp.k)) (= tptp.j tptp.k)) :rule resolution :premises (t743 t757))
% 0.55/0.72 (step t759 (cl (tptp.element tptp.k tptp.m) (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.j tptp.k))) :rule contraction :premises (t758))
% 0.55/0.72 (step t760 (cl (= tptp.j tptp.k) (= tptp.m tptp.k) (not (tptp.element tptp.j tptp.k)) (tptp.element tptp.k tptp.m)) :rule reordering :premises (t759))
% 0.55/0.72 (step t761 (cl (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (not (= tptp.j tptp.k)) (not (tptp.element tptp.n tptp.k))) :rule and_neg)
% 0.55/0.72 (step t762 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t763)
% 0.55/0.72 (assume t763.a0 (= tptp.j tptp.k))
% 0.55/0.72 (assume t763.a1 (tptp.element tptp.n tptp.k))
% 0.55/0.72 (step t763.t1 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j)) (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t763.t2)
% 0.55/0.72 (assume t763.t2.a0 (tptp.element tptp.n tptp.k))
% 0.55/0.72 (assume t763.t2.a1 (= tptp.j tptp.k))
% 0.55/0.72 (step t763.t2.t1 (cl (= (= (tptp.element tptp.n tptp.j) true) (tptp.element tptp.n tptp.j))) :rule equiv_simplify)
% 0.55/0.72 (step t763.t2.t2 (cl (not (= (tptp.element tptp.n tptp.j) true)) (tptp.element tptp.n tptp.j)) :rule equiv1 :premises (t763.t2.t1))
% 0.55/0.72 (step t763.t2.t3 (cl (= tptp.n tptp.n)) :rule refl)
% 0.55/0.72 (step t763.t2.t4 (cl (= tptp.k tptp.j)) :rule symm :premises (t763.t2.a1))
% 0.55/0.72 (step t763.t2.t5 (cl (= tptp.j tptp.k)) :rule symm :premises (t763.t2.t4))
% 0.55/0.72 (step t763.t2.t6 (cl (= (tptp.element tptp.n tptp.j) (tptp.element tptp.n tptp.k))) :rule cong :premises (t763.t2.t3 t763.t2.t5))
% 0.55/0.72 (step t763.t2.t7 (cl (= (= (tptp.element tptp.n tptp.k) true) (tptp.element tptp.n tptp.k))) :rule equiv_simplify)
% 0.55/0.72 (step t763.t2.t8 (cl (= (tptp.element tptp.n tptp.k) true) (not (tptp.element tptp.n tptp.k))) :rule equiv2 :premises (t763.t2.t7))
% 0.55/0.72 (step t763.t2.t9 (cl (= (tptp.element tptp.n tptp.k) true)) :rule resolution :premises (t763.t2.t8 t763.t2.a0))
% 0.55/0.72 (step t763.t2.t10 (cl (= (tptp.element tptp.n tptp.j) true)) :rule trans :premises (t763.t2.t6 t763.t2.t9))
% 0.55/0.72 (step t763.t2.t11 (cl (tptp.element tptp.n tptp.j)) :rule resolution :premises (t763.t2.t2 t763.t2.t10))
% 0.55/0.72 (step t763.t2 (cl (not (tptp.element tptp.n tptp.k)) (not (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j)) :rule subproof :discharge (t763.t2.a0 t763.t2.a1))
% 0.55/0.72 (step t763.t3 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t763.t4 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t763.t5 (cl (tptp.element tptp.n tptp.j) (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)))) :rule resolution :premises (t763.t2 t763.t3 t763.t4))
% 0.55/0.72 (step t763.t6 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.n tptp.j)) :rule reordering :premises (t763.t5))
% 0.55/0.72 (step t763.t7 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.n tptp.j)) :rule contraction :premises (t763.t6))
% 0.55/0.72 (step t763.t8 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j)) (tptp.element tptp.n tptp.j)) :rule resolution :premises (t763.t1 t763.t7))
% 0.55/0.72 (step t763.t9 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j)) (not (tptp.element tptp.n tptp.j))) :rule implies_neg2)
% 0.55/0.72 (step t763.t10 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j)) (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j))) :rule resolution :premises (t763.t8 t763.t9))
% 0.55/0.72 (step t763.t11 (cl (=> (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.n tptp.j))) :rule contraction :premises (t763.t10))
% 0.55/0.72 (step t763.t12 (cl (not (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.n tptp.j)) :rule implies :premises (t763.t11))
% 0.55/0.72 (step t763.t13 (cl (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k)) (not (tptp.element tptp.n tptp.k)) (not (= tptp.j tptp.k))) :rule and_neg)
% 0.55/0.72 (step t763.t14 (cl (and (tptp.element tptp.n tptp.k) (= tptp.j tptp.k))) :rule resolution :premises (t763.t13 t763.a1 t763.a0))
% 0.55/0.72 (step t763.t15 (cl (tptp.element tptp.n tptp.j)) :rule resolution :premises (t763.t12 t763.t14))
% 0.55/0.72 (step t763 (cl (not (= tptp.j tptp.k)) (not (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) :rule subproof :discharge (t763.a0 t763.a1))
% 0.55/0.72 (step t764 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t765 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t766 (cl (tptp.element tptp.n tptp.j) (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)))) :rule resolution :premises (t763 t764 t765))
% 0.55/0.72 (step t767 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.j)) :rule reordering :premises (t766))
% 0.55/0.72 (step t768 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.j)) :rule contraction :premises (t767))
% 0.55/0.72 (step t769 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) (tptp.element tptp.n tptp.j)) :rule resolution :premises (t762 t768))
% 0.55/0.72 (step t770 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) (not (tptp.element tptp.n tptp.j))) :rule implies_neg2)
% 0.55/0.72 (step t771 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j))) :rule resolution :premises (t769 t770))
% 0.55/0.72 (step t772 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j))) :rule contraction :premises (t771))
% 0.55/0.72 (step t773 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.n tptp.k))) (tptp.element tptp.n tptp.j)) :rule implies :premises (t772))
% 0.55/0.72 (step t774 (cl (not (= tptp.j tptp.k)) (not (tptp.element tptp.n tptp.k)) (tptp.element tptp.n tptp.j)) :rule resolution :premises (t761 t773))
% 0.55/0.72 (step t775 (cl (not (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j)))) (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j))) :rule or_pos)
% 0.55/0.72 (step t776 (cl (= tptp.n tptp.k) (= tptp.n tptp.j) (not (tptp.element tptp.n tptp.j)) (not (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j))))) :rule reordering :premises (t775))
% 0.55/0.72 (step t777 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j)))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j))))) :rule equiv_pos2)
% 0.55/0.72 (step t778 (cl (= (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))) :rule refl)
% 0.55/0.72 (step t779 (cl (= (= tptp.j tptp.n) (= tptp.n tptp.j))) :rule all_simplify)
% 0.55/0.72 (step t780 (cl (= (not (tptp.element tptp.n tptp.j)) (not (tptp.element tptp.n tptp.j)))) :rule refl)
% 0.55/0.72 (step t781 (cl (= (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j))))) :rule cong :premises (t779 t354 t780))
% 0.55/0.72 (step t782 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j)))))) :rule cong :premises (t778 t781))
% 0.55/0.72 (step t783 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t784)
% 0.55/0.72 (assume t784.a0 (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))
% 0.55/0.72 (step t784.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))))) :rule forall_inst :args ((:= Y tptp.n)))
% 0.55/0.72 (step t784.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) :rule or :premises (t784.t1))
% 0.55/0.72 (step t784.t3 (cl (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) :rule resolution :premises (t784.t2 t784.a0))
% 0.55/0.72 (step t784 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) :rule subproof :discharge (t784.a0))
% 0.55/0.72 (step t785 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) :rule resolution :premises (t783 t784))
% 0.55/0.72 (step t786 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (not (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))))) :rule implies_neg2)
% 0.55/0.72 (step t787 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))))) :rule resolution :premises (t785 t786))
% 0.55/0.72 (step t788 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.n) (= tptp.k tptp.n) (not (tptp.element tptp.n tptp.j))))) :rule contraction :premises (t787))
% 0.55/0.72 (step t789 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j))))) :rule resolution :premises (t777 t782 t788))
% 0.55/0.72 (step t790 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j)))) :rule implies :premises (t789))
% 0.55/0.72 (step t791 (cl (not (= (forall ((Y $$unsorted)) (or (= Y tptp.j) (= Y tptp.k) (not (tptp.element Y tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))) (not (forall ((Y $$unsorted)) (or (= Y tptp.j) (= Y tptp.k) (not (tptp.element Y tptp.j))))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule equiv_pos2)
% 0.55/0.72 (anchor :step t792 :args ((Y $$unsorted) (:= Y Y)))
% 0.55/0.72 (step t792.t1 (cl (= Y Y)) :rule refl)
% 0.55/0.72 (step t792.t2 (cl (= (= Y tptp.j) (= tptp.j Y))) :rule all_simplify)
% 0.55/0.72 (step t792.t3 (cl (= (= Y tptp.k) (= tptp.k Y))) :rule all_simplify)
% 0.55/0.72 (step t792.t4 (cl (= (not (tptp.element Y tptp.j)) (not (tptp.element Y tptp.j)))) :rule refl)
% 0.55/0.72 (step t792.t5 (cl (= (or (= Y tptp.j) (= Y tptp.k) (not (tptp.element Y tptp.j))) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule cong :premises (t792.t2 t792.t3 t792.t4))
% 0.55/0.72 (step t792 (cl (= (forall ((Y $$unsorted)) (or (= Y tptp.j) (= Y tptp.k) (not (tptp.element Y tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))) :rule bind)
% 0.55/0.72 (step t793 (cl (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule resolution :premises (t791 t792 a2))
% 0.55/0.72 (step t794 (cl (or (= tptp.n tptp.j) (= tptp.n tptp.k) (not (tptp.element tptp.n tptp.j)))) :rule resolution :premises (t790 t793))
% 0.55/0.72 (step t795 (cl (not (= (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (not (= tptp.n tptp.j))))) (not (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j)))) (or (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (not (= tptp.n tptp.j)))) :rule equiv_pos2)
% 0.55/0.72 (step t796 (cl (= (not (= tptp.j tptp.k)) (not (= tptp.j tptp.k)))) :rule refl)
% 0.55/0.72 (step t797 (cl (= (= (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k)) true) (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t798 (cl (not (= (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k)) true)) (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k))) :rule equiv1 :premises (t797))
% 0.55/0.72 (step t799 (cl (= (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k)) (= (= tptp.n tptp.k) (not (not (= tptp.n tptp.k)))))) :rule all_simplify)
% 0.55/0.72 (step t800 (cl (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k))) :rule all_simplify)
% 0.55/0.72 (step t801 (cl (= (= (= tptp.n tptp.k) (not (not (= tptp.n tptp.k)))) (= (= tptp.n tptp.k) (= tptp.n tptp.k)))) :rule cong :premises (t81 t800))
% 0.55/0.72 (step t802 (cl (= (= (= tptp.n tptp.k) (= tptp.n tptp.k)) true)) :rule all_simplify)
% 0.55/0.72 (step t803 (cl (= (= (= tptp.n tptp.k) (not (not (= tptp.n tptp.k)))) true)) :rule trans :premises (t801 t802))
% 0.55/0.72 (step t804 (cl (= (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k)) true)) :rule trans :premises (t799 t803))
% 0.55/0.72 (step t805 (cl (= (not (not (= tptp.n tptp.k))) (= tptp.n tptp.k))) :rule resolution :premises (t798 t804))
% 0.55/0.72 (step t806 (cl (= (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (not (= tptp.n tptp.j))))) :rule cong :premises (t796 t805 t13))
% 0.55/0.72 (step t807 (cl (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k)))) :rule and_neg)
% 0.55/0.72 (step t808 (cl (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t809)
% 0.55/0.72 (assume t809.a0 (= tptp.j tptp.k))
% 0.55/0.72 (assume t809.a1 (not (= tptp.n tptp.k)))
% 0.55/0.72 (step t809.t1 (cl (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t809.t2)
% 0.55/0.72 (assume t809.t2.a0 (not (= tptp.n tptp.k)))
% 0.55/0.72 (assume t809.t2.a1 (= tptp.j tptp.k))
% 0.55/0.72 (step t809.t2.t1 (cl (= (= (= tptp.n tptp.j) false) (not (= tptp.n tptp.j)))) :rule equiv_simplify)
% 0.55/0.72 (step t809.t2.t2 (cl (not (= (= tptp.n tptp.j) false)) (not (= tptp.n tptp.j))) :rule equiv1 :premises (t809.t2.t1))
% 0.55/0.72 (step t809.t2.t3 (cl (= tptp.n tptp.n)) :rule refl)
% 0.55/0.72 (step t809.t2.t4 (cl (= tptp.k tptp.j)) :rule symm :premises (t809.t2.a1))
% 0.55/0.72 (step t809.t2.t5 (cl (= tptp.j tptp.k)) :rule symm :premises (t809.t2.t4))
% 0.55/0.72 (step t809.t2.t6 (cl (= (= tptp.n tptp.j) (= tptp.n tptp.k))) :rule cong :premises (t809.t2.t3 t809.t2.t5))
% 0.55/0.72 (step t809.t2.t7 (cl (= (= (= tptp.n tptp.k) false) (not (= tptp.n tptp.k)))) :rule equiv_simplify)
% 0.55/0.72 (step t809.t2.t8 (cl (= (= tptp.n tptp.k) false) (not (not (= tptp.n tptp.k)))) :rule equiv2 :premises (t809.t2.t7))
% 0.55/0.72 (step t809.t2.t9 (cl (not (not (not (= tptp.n tptp.k)))) (= tptp.n tptp.k)) :rule not_not)
% 0.55/0.72 (step t809.t2.t10 (cl (= (= tptp.n tptp.k) false) (= tptp.n tptp.k)) :rule resolution :premises (t809.t2.t8 t809.t2.t9))
% 0.55/0.72 (step t809.t2.t11 (cl (= (= tptp.n tptp.k) false)) :rule resolution :premises (t809.t2.t10 t809.t2.a0))
% 0.55/0.72 (step t809.t2.t12 (cl (= (= tptp.n tptp.j) false)) :rule trans :premises (t809.t2.t6 t809.t2.t11))
% 0.55/0.72 (step t809.t2.t13 (cl (not (= tptp.n tptp.j))) :rule resolution :premises (t809.t2.t2 t809.t2.t12))
% 0.55/0.72 (step t809.t2 (cl (not (not (= tptp.n tptp.k))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) :rule subproof :discharge (t809.t2.a0 t809.t2.a1))
% 0.55/0.72 (step t809.t3 (cl (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (= tptp.n tptp.k))) :rule and_pos)
% 0.55/0.72 (step t809.t4 (cl (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t809.t5 (cl (not (= tptp.n tptp.j)) (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)))) :rule resolution :premises (t809.t2 t809.t3 t809.t4))
% 0.55/0.72 (step t809.t6 (cl (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) :rule reordering :premises (t809.t5))
% 0.55/0.72 (step t809.t7 (cl (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) :rule contraction :premises (t809.t6))
% 0.55/0.72 (step t809.t8 (cl (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) (not (= tptp.n tptp.j))) :rule resolution :premises (t809.t1 t809.t7))
% 0.55/0.72 (step t809.t9 (cl (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) (not (not (= tptp.n tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t809.t10 (cl (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j)))) :rule resolution :premises (t809.t8 t809.t9))
% 0.55/0.72 (step t809.t11 (cl (=> (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (= tptp.n tptp.j)))) :rule contraction :premises (t809.t10))
% 0.55/0.72 (step t809.t12 (cl (not (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) (not (= tptp.n tptp.j))) :rule implies :premises (t809.t11))
% 0.55/0.72 (step t809.t13 (cl (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.j tptp.k))) :rule and_neg)
% 0.55/0.72 (step t809.t14 (cl (and (not (= tptp.n tptp.k)) (= tptp.j tptp.k))) :rule resolution :premises (t809.t13 t809.a1 t809.a0))
% 0.55/0.72 (step t809.t15 (cl (not (= tptp.n tptp.j))) :rule resolution :premises (t809.t12 t809.t14))
% 0.55/0.72 (step t809 (cl (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) :rule subproof :discharge (t809.a0 t809.a1))
% 0.55/0.72 (step t810 (cl (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t811 (cl (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (= tptp.n tptp.k))) :rule and_pos)
% 0.55/0.72 (step t812 (cl (not (= tptp.n tptp.j)) (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))))) :rule resolution :premises (t809 t810 t811))
% 0.55/0.72 (step t813 (cl (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (= tptp.n tptp.j))) :rule reordering :premises (t812))
% 0.55/0.72 (step t814 (cl (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (= tptp.n tptp.j))) :rule contraction :premises (t813))
% 0.55/0.72 (step t815 (cl (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (not (= tptp.n tptp.j))) :rule resolution :premises (t808 t814))
% 0.55/0.72 (step t816 (cl (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (not (not (= tptp.n tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t817 (cl (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j)))) :rule resolution :premises (t815 t816))
% 0.55/0.72 (step t818 (cl (=> (and (= tptp.j tptp.k) (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j)))) :rule contraction :premises (t817))
% 0.55/0.72 (step t819 (cl (not (and (= tptp.j tptp.k) (not (= tptp.n tptp.k)))) (not (= tptp.n tptp.j))) :rule implies :premises (t818))
% 0.55/0.72 (step t820 (cl (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) :rule resolution :premises (t807 t819))
% 0.55/0.72 (step t821 (cl (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (not (not (= tptp.j tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t822 (cl (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (not (not (not (= tptp.n tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t823 (cl (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (not (not (= tptp.n tptp.j)))) :rule or_neg)
% 0.55/0.72 (step t824 (cl (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j))) (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j)))) :rule resolution :premises (t820 t821 t822 t823))
% 0.55/0.72 (step t825 (cl (or (not (= tptp.j tptp.k)) (not (not (= tptp.n tptp.k))) (not (= tptp.n tptp.j)))) :rule contraction :premises (t824))
% 0.55/0.72 (step t826 (cl (or (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (not (= tptp.n tptp.j)))) :rule resolution :premises (t795 t806 t825))
% 0.55/0.72 (step t827 (cl (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (not (= tptp.n tptp.j))) :rule or :premises (t826))
% 0.55/0.72 (step t828 (cl (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.j))) :rule reordering :premises (t827))
% 0.55/0.72 (step t829 (cl (not (= tptp.j tptp.k)) (= tptp.n tptp.k) (= tptp.n tptp.k) (not (= tptp.j tptp.k)) (= tptp.n tptp.k)) :rule resolution :premises (t774 t776 t794 t828 t383))
% 0.55/0.72 (step t830 (cl (not (= tptp.j tptp.k)) (= tptp.n tptp.k)) :rule contraction :premises (t829))
% 0.55/0.72 (step t831 (cl (not (= (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (or (= tptp.n tptp.m) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))))) (not (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)))) (or (= tptp.n tptp.m) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)))) :rule equiv_pos2)
% 0.55/0.72 (step t832 (cl (= (= (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m)) true) (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t833 (cl (not (= (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m)) true)) (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m))) :rule equiv1 :premises (t832))
% 0.55/0.72 (step t834 (cl (= (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m)) (= (= tptp.n tptp.m) (not (not (= tptp.n tptp.m)))))) :rule all_simplify)
% 0.55/0.72 (step t835 (cl (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m))) :rule all_simplify)
% 0.55/0.72 (step t836 (cl (= (= (= tptp.n tptp.m) (not (not (= tptp.n tptp.m)))) (= (= tptp.n tptp.m) (= tptp.n tptp.m)))) :rule cong :premises (t83 t835))
% 0.55/0.72 (step t837 (cl (= (= (= tptp.n tptp.m) (= tptp.n tptp.m)) true)) :rule all_simplify)
% 0.55/0.72 (step t838 (cl (= (= (= tptp.n tptp.m) (not (not (= tptp.n tptp.m)))) true)) :rule trans :premises (t836 t837))
% 0.55/0.72 (step t839 (cl (= (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m)) true)) :rule trans :premises (t834 t838))
% 0.55/0.72 (step t840 (cl (= (not (not (= tptp.n tptp.m))) (= tptp.n tptp.m))) :rule resolution :premises (t833 t839))
% 0.55/0.72 (step t841 (cl (= (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (or (= tptp.n tptp.m) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))))) :rule cong :premises (t840 t796 t2 t672))
% 0.55/0.72 (step t842 (cl (not (= (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))))) (not (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)))) :rule equiv_pos2)
% 0.55/0.72 (step t843 (cl (= (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)))) :rule refl)
% 0.55/0.72 (step t844 (cl (= (= (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))))) :rule equiv_simplify)
% 0.55/0.72 (step t845 (cl (= (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (not (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))))) :rule equiv2 :premises (t844))
% 0.55/0.72 (step t846 (cl (not (not (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))))) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule not_not)
% 0.55/0.72 (step t847 (cl (= (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule resolution :premises (t845 t846))
% 0.55/0.72 (step t848 (cl (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t849)
% 0.55/0.72 (assume t849.a0 (= tptp.j tptp.k))
% 0.55/0.72 (assume t849.a1 (= tptp.n tptp.k))
% 0.55/0.72 (assume t849.a2 (= tptp.m tptp.j))
% 0.55/0.72 (assume t849.a3 (not (= tptp.n tptp.m)))
% 0.55/0.72 (step t849.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 0.55/0.72 (step t849.t2 (cl (= (= false true) false)) :rule all_simplify)
% 0.55/0.72 (step t849.t3 (cl (= (= (= tptp.n tptp.m) false) (not (= tptp.n tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t849.t4 (cl (= (= tptp.n tptp.m) false) (not (not (= tptp.n tptp.m)))) :rule equiv2 :premises (t849.t3))
% 0.55/0.72 (step t849.t5 (cl (not (not (not (= tptp.n tptp.m)))) (= tptp.n tptp.m)) :rule not_not)
% 0.55/0.72 (step t849.t6 (cl (= (= tptp.n tptp.m) false) (= tptp.n tptp.m)) :rule resolution :premises (t849.t4 t849.t5))
% 0.55/0.72 (step t849.t7 (cl (= (= tptp.n tptp.m) false)) :rule resolution :premises (t849.t6 t849.a3))
% 0.55/0.72 (step t849.t8 (cl (= false (= tptp.n tptp.m))) :rule symm :premises (t849.t7))
% 0.55/0.72 (step t849.t9 (cl (= (= (= tptp.n tptp.m) true) (= tptp.n tptp.m))) :rule equiv_simplify)
% 0.55/0.72 (step t849.t10 (cl (= (= tptp.n tptp.m) true) (not (= tptp.n tptp.m))) :rule equiv2 :premises (t849.t9))
% 0.55/0.72 (step t849.t11 (cl (= tptp.k tptp.n)) :rule symm :premises (t849.a1))
% 0.55/0.72 (step t849.t12 (cl (= tptp.n tptp.k)) :rule symm :premises (t849.t11))
% 0.55/0.72 (step t849.t13 (cl (= tptp.k tptp.j)) :rule symm :premises (t849.a0))
% 0.55/0.72 (step t849.t14 (cl (= tptp.n tptp.j)) :rule trans :premises (t849.t12 t849.t13))
% 0.55/0.72 (step t849.t15 (cl (= tptp.j tptp.k)) :rule symm :premises (t849.t13))
% 0.55/0.72 (step t849.t16 (cl (= tptp.j tptp.m)) :rule symm :premises (t849.a2))
% 0.55/0.72 (step t849.t17 (cl (= tptp.m tptp.j)) :rule symm :premises (t849.t16))
% 0.55/0.72 (step t849.t18 (cl (= tptp.m tptp.k)) :rule trans :premises (t849.t17 t849.t15))
% 0.55/0.72 (step t849.t19 (cl (= tptp.k tptp.m)) :rule symm :premises (t849.t18))
% 0.55/0.72 (step t849.t20 (cl (= tptp.n tptp.m)) :rule trans :premises (t849.t14 t849.t15 t849.t19))
% 0.55/0.72 (step t849.t21 (cl (= (= tptp.n tptp.m) true)) :rule resolution :premises (t849.t10 t849.t20))
% 0.55/0.72 (step t849.t22 (cl (= false true)) :rule trans :premises (t849.t8 t849.t21))
% 0.55/0.72 (step t849.t23 (cl false) :rule resolution :premises (t849.t1 t849.t2 t849.t22))
% 0.55/0.72 (step t849 (cl (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (= tptp.n tptp.m))) false) :rule subproof :discharge (t849.a0 t849.a1 t849.a2 t849.a3))
% 0.55/0.72 (step t850 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t851 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t852 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (= tptp.m tptp.j)) :rule and_pos)
% 0.55/0.72 (step t853 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (= tptp.n tptp.m))) :rule and_pos)
% 0.55/0.72 (step t854 (cl false (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule resolution :premises (t849 t850 t851 t852 t853))
% 0.55/0.72 (step t855 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) false) :rule reordering :premises (t854))
% 0.55/0.72 (step t856 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) false) :rule contraction :premises (t855))
% 0.55/0.72 (step t857 (cl (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) false) :rule resolution :premises (t848 t856))
% 0.55/0.72 (step t858 (cl (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t859 (cl (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false)) :rule resolution :premises (t857 t858))
% 0.55/0.72 (step t860 (cl (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false)) :rule contraction :premises (t859))
% 0.55/0.72 (step t861 (cl (= (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))))) :rule implies_simplify)
% 0.55/0.72 (step t862 (cl (not (=> (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false)) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule equiv1 :premises (t861))
% 0.55/0.72 (step t863 (cl (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule resolution :premises (t860 t862))
% 0.55/0.72 (step t864 (cl (= (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) false)) :rule resolution :premises (t847 t863))
% 0.55/0.72 (step t865 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) false))) :rule cong :premises (t843 t864))
% 0.55/0.72 (step t866 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) false) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))))) :rule all_simplify)
% 0.55/0.72 (step t867 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))))) :rule trans :premises (t865 t866))
% 0.55/0.72 (step t868 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t869)
% 0.55/0.72 (assume t869.a0 (not (= tptp.n tptp.m)))
% 0.55/0.72 (assume t869.a1 (= tptp.j tptp.k))
% 0.55/0.72 (assume t869.a2 (= tptp.n tptp.k))
% 0.55/0.72 (assume t869.a3 (= tptp.m tptp.j))
% 0.55/0.72 (step t869.t1 (cl (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (not (not (= tptp.n tptp.m)))) :rule and_neg)
% 0.55/0.72 (step t869.t2 (cl (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule resolution :premises (t869.t1 t869.a1 t869.a2 t869.a3 t869.a0))
% 0.55/0.72 (step t869 (cl (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule subproof :discharge (t869.a0 t869.a1 t869.a2 t869.a3))
% 0.55/0.72 (step t870 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (= tptp.n tptp.m))) :rule and_pos)
% 0.55/0.72 (step t871 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t872 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t873 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (= tptp.m tptp.j)) :rule and_pos)
% 0.55/0.72 (step t874 (cl (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)))) :rule resolution :premises (t869 t870 t871 t872 t873))
% 0.55/0.72 (step t875 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule reordering :premises (t874))
% 0.55/0.72 (step t876 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j))) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule contraction :premises (t875))
% 0.55/0.72 (step t877 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) :rule resolution :premises (t868 t876))
% 0.55/0.72 (step t878 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (not (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule implies_neg2)
% 0.55/0.72 (step t879 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m)))) (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule resolution :premises (t877 t878))
% 0.55/0.72 (step t880 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)) (and (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j) (not (= tptp.n tptp.m))))) :rule contraction :premises (t879))
% 0.55/0.72 (step t881 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.j tptp.k) (= tptp.n tptp.k) (= tptp.m tptp.j)))) :rule resolution :premises (t842 t867 t880))
% 0.55/0.72 (step t882 (cl (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) :rule not_and :premises (t881))
% 0.55/0.72 (step t883 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (not (not (not (= tptp.n tptp.m))))) :rule or_neg)
% 0.55/0.72 (step t884 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (not (not (= tptp.j tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t885 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t886 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (not (not (= tptp.m tptp.j)))) :rule or_neg)
% 0.55/0.72 (step t887 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)))) :rule resolution :premises (t882 t883 t884 t885 t886))
% 0.55/0.72 (step t888 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)))) :rule contraction :premises (t887))
% 0.55/0.72 (step t889 (cl (or (= tptp.n tptp.m) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j)))) :rule resolution :premises (t831 t841 t888))
% 0.55/0.72 (step t890 (cl (= tptp.n tptp.m) (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.j))) :rule or :premises (t889))
% 0.55/0.72 (step t891 (cl (not (= tptp.n tptp.m))) :rule not_symm :premises (a0))
% 0.55/0.72 (step t892 (cl (not (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j)))) (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j))) :rule or_pos)
% 0.55/0.72 (step t893 (cl (= tptp.m tptp.k) (= tptp.m tptp.j) (not (tptp.element tptp.m tptp.j)) (not (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j))))) :rule reordering :premises (t892))
% 0.55/0.72 (step t894 (cl (not (= (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j)))))) (not (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j))))) :rule equiv_pos2)
% 0.55/0.72 (step t895 (cl (= (= tptp.j tptp.m) (= tptp.m tptp.j))) :rule all_simplify)
% 0.55/0.72 (step t896 (cl (= (not (tptp.element tptp.m tptp.j)) (not (tptp.element tptp.m tptp.j)))) :rule refl)
% 0.55/0.72 (step t897 (cl (= (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j))))) :rule cong :premises (t895 t84 t896))
% 0.55/0.72 (step t898 (cl (= (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j)))))) :rule cong :premises (t778 t897))
% 0.55/0.72 (step t899 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t900)
% 0.55/0.72 (assume t900.a0 (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))
% 0.55/0.72 (step t900.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))))) :rule forall_inst :args ((:= Y tptp.m)))
% 0.55/0.72 (step t900.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) :rule or :premises (t900.t1))
% 0.55/0.72 (step t900.t3 (cl (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) :rule resolution :premises (t900.t2 t900.a0))
% 0.55/0.72 (step t900 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) :rule subproof :discharge (t900.a0))
% 0.55/0.72 (step t901 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) :rule resolution :premises (t899 t900))
% 0.55/0.72 (step t902 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (not (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))))) :rule implies_neg2)
% 0.55/0.72 (step t903 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))))) :rule resolution :premises (t901 t902))
% 0.55/0.72 (step t904 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j tptp.m) (= tptp.k tptp.m) (not (tptp.element tptp.m tptp.j))))) :rule contraction :premises (t903))
% 0.55/0.72 (step t905 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j))))) :rule resolution :premises (t894 t898 t904))
% 0.55/0.72 (step t906 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j)))) :rule implies :premises (t905))
% 0.55/0.72 (step t907 (cl (or (= tptp.m tptp.j) (= tptp.m tptp.k) (not (tptp.element tptp.m tptp.j)))) :rule resolution :premises (t906 t793))
% 0.55/0.72 (step t908 (cl (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (not (= tptp.j tptp.k)) (not (tptp.element tptp.m tptp.k))) :rule and_neg)
% 0.55/0.72 (step t909 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t910)
% 0.55/0.72 (assume t910.a0 (= tptp.j tptp.k))
% 0.55/0.72 (assume t910.a1 (tptp.element tptp.m tptp.k))
% 0.55/0.72 (step t910.t1 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j)) (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t910.t2)
% 0.55/0.72 (assume t910.t2.a0 (tptp.element tptp.m tptp.k))
% 0.55/0.72 (assume t910.t2.a1 (= tptp.j tptp.k))
% 0.55/0.72 (step t910.t2.t1 (cl (= (= (tptp.element tptp.m tptp.j) true) (tptp.element tptp.m tptp.j))) :rule equiv_simplify)
% 0.55/0.72 (step t910.t2.t2 (cl (not (= (tptp.element tptp.m tptp.j) true)) (tptp.element tptp.m tptp.j)) :rule equiv1 :premises (t910.t2.t1))
% 0.55/0.72 (step t910.t2.t3 (cl (= tptp.m tptp.m)) :rule refl)
% 0.55/0.72 (step t910.t2.t4 (cl (= tptp.k tptp.j)) :rule symm :premises (t910.t2.a1))
% 0.55/0.72 (step t910.t2.t5 (cl (= tptp.j tptp.k)) :rule symm :premises (t910.t2.t4))
% 0.55/0.72 (step t910.t2.t6 (cl (= (tptp.element tptp.m tptp.j) (tptp.element tptp.m tptp.k))) :rule cong :premises (t910.t2.t3 t910.t2.t5))
% 0.55/0.72 (step t910.t2.t7 (cl (= (= (tptp.element tptp.m tptp.k) true) (tptp.element tptp.m tptp.k))) :rule equiv_simplify)
% 0.55/0.72 (step t910.t2.t8 (cl (= (tptp.element tptp.m tptp.k) true) (not (tptp.element tptp.m tptp.k))) :rule equiv2 :premises (t910.t2.t7))
% 0.55/0.72 (step t910.t2.t9 (cl (= (tptp.element tptp.m tptp.k) true)) :rule resolution :premises (t910.t2.t8 t910.t2.a0))
% 0.55/0.72 (step t910.t2.t10 (cl (= (tptp.element tptp.m tptp.j) true)) :rule trans :premises (t910.t2.t6 t910.t2.t9))
% 0.55/0.72 (step t910.t2.t11 (cl (tptp.element tptp.m tptp.j)) :rule resolution :premises (t910.t2.t2 t910.t2.t10))
% 0.55/0.72 (step t910.t2 (cl (not (tptp.element tptp.m tptp.k)) (not (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j)) :rule subproof :discharge (t910.t2.a0 t910.t2.a1))
% 0.55/0.72 (step t910.t3 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t910.t4 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t910.t5 (cl (tptp.element tptp.m tptp.j) (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)))) :rule resolution :premises (t910.t2 t910.t3 t910.t4))
% 0.55/0.72 (step t910.t6 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.m tptp.j)) :rule reordering :premises (t910.t5))
% 0.55/0.72 (step t910.t7 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.m tptp.j)) :rule contraction :premises (t910.t6))
% 0.55/0.72 (step t910.t8 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j)) (tptp.element tptp.m tptp.j)) :rule resolution :premises (t910.t1 t910.t7))
% 0.55/0.72 (step t910.t9 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j)) (not (tptp.element tptp.m tptp.j))) :rule implies_neg2)
% 0.55/0.72 (step t910.t10 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j)) (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j))) :rule resolution :premises (t910.t8 t910.t9))
% 0.55/0.72 (step t910.t11 (cl (=> (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (tptp.element tptp.m tptp.j))) :rule contraction :premises (t910.t10))
% 0.55/0.72 (step t910.t12 (cl (not (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) (tptp.element tptp.m tptp.j)) :rule implies :premises (t910.t11))
% 0.55/0.72 (step t910.t13 (cl (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k)) (not (tptp.element tptp.m tptp.k)) (not (= tptp.j tptp.k))) :rule and_neg)
% 0.55/0.72 (step t910.t14 (cl (and (tptp.element tptp.m tptp.k) (= tptp.j tptp.k))) :rule resolution :premises (t910.t13 t910.a1 t910.a0))
% 0.55/0.72 (step t910.t15 (cl (tptp.element tptp.m tptp.j)) :rule resolution :premises (t910.t12 t910.t14))
% 0.55/0.72 (step t910 (cl (not (= tptp.j tptp.k)) (not (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) :rule subproof :discharge (t910.a0 t910.a1))
% 0.55/0.72 (step t911 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (= tptp.j tptp.k)) :rule and_pos)
% 0.55/0.72 (step t912 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (tptp.element tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t913 (cl (tptp.element tptp.m tptp.j) (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)))) :rule resolution :premises (t910 t911 t912))
% 0.55/0.72 (step t914 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (tptp.element tptp.m tptp.j)) :rule reordering :premises (t913))
% 0.55/0.72 (step t915 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (tptp.element tptp.m tptp.j)) :rule contraction :premises (t914))
% 0.55/0.72 (step t916 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) (tptp.element tptp.m tptp.j)) :rule resolution :premises (t909 t915))
% 0.55/0.72 (step t917 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) (not (tptp.element tptp.m tptp.j))) :rule implies_neg2)
% 0.55/0.72 (step t918 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j))) :rule resolution :premises (t916 t917))
% 0.55/0.72 (step t919 (cl (=> (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j))) :rule contraction :premises (t918))
% 0.55/0.72 (step t920 (cl (not (and (= tptp.j tptp.k) (tptp.element tptp.m tptp.k))) (tptp.element tptp.m tptp.j)) :rule implies :premises (t919))
% 0.55/0.72 (step t921 (cl (not (= tptp.j tptp.k)) (not (tptp.element tptp.m tptp.k)) (tptp.element tptp.m tptp.j)) :rule resolution :premises (t908 t920))
% 0.55/0.72 (step t922 (cl (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (= tptp.m tptp.k) (not (= tptp.j tptp.k)) (= tptp.m tptp.k)) :rule resolution :premises (t890 t891 t893 t907 t921 t456))
% 0.55/0.72 (step t923 (cl (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (= tptp.m tptp.k)) :rule contraction :premises (t922))
% 0.55/0.72 (step t924 (cl (not (= (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (or (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))))) (not (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)))) (or (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)))) :rule equiv_pos2)
% 0.55/0.72 (step t925 (cl (= (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (or (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))))) :rule cong :premises (t840 t388 t2))
% 0.55/0.72 (step t926 (cl (not (= (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))))) (not (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)))) :rule equiv_pos2)
% 0.55/0.72 (step t927 (cl (= (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)))) :rule refl)
% 0.55/0.72 (step t928 (cl (= (= (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))))) :rule equiv_simplify)
% 0.55/0.72 (step t929 (cl (= (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (not (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))))) :rule equiv2 :premises (t928))
% 0.55/0.72 (step t930 (cl (not (not (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))))) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule not_not)
% 0.55/0.72 (step t931 (cl (= (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule resolution :premises (t929 t930))
% 0.55/0.72 (step t932 (cl (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t933)
% 0.55/0.72 (assume t933.a0 (= tptp.n tptp.k))
% 0.55/0.72 (assume t933.a1 (= tptp.m tptp.k))
% 0.55/0.72 (assume t933.a2 (not (= tptp.n tptp.m)))
% 0.55/0.72 (step t933.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 0.55/0.72 (step t933.t2 (cl (= (= false true) false)) :rule all_simplify)
% 0.55/0.72 (step t933.t3 (cl (= (= (= tptp.n tptp.m) false) (not (= tptp.n tptp.m)))) :rule equiv_simplify)
% 0.55/0.72 (step t933.t4 (cl (= (= tptp.n tptp.m) false) (not (not (= tptp.n tptp.m)))) :rule equiv2 :premises (t933.t3))
% 0.55/0.72 (step t933.t5 (cl (not (not (not (= tptp.n tptp.m)))) (= tptp.n tptp.m)) :rule not_not)
% 0.55/0.72 (step t933.t6 (cl (= (= tptp.n tptp.m) false) (= tptp.n tptp.m)) :rule resolution :premises (t933.t4 t933.t5))
% 0.55/0.72 (step t933.t7 (cl (= (= tptp.n tptp.m) false)) :rule resolution :premises (t933.t6 t933.a2))
% 0.55/0.72 (step t933.t8 (cl (= false (= tptp.n tptp.m))) :rule symm :premises (t933.t7))
% 0.55/0.72 (step t933.t9 (cl (= (= (= tptp.n tptp.m) true) (= tptp.n tptp.m))) :rule equiv_simplify)
% 0.55/0.72 (step t933.t10 (cl (= (= tptp.n tptp.m) true) (not (= tptp.n tptp.m))) :rule equiv2 :premises (t933.t9))
% 0.55/0.72 (step t933.t11 (cl (= tptp.k tptp.n)) :rule symm :premises (t933.a0))
% 0.55/0.72 (step t933.t12 (cl (= tptp.n tptp.k)) :rule symm :premises (t933.t11))
% 0.55/0.72 (step t933.t13 (cl (= tptp.k tptp.m)) :rule symm :premises (t933.a1))
% 0.55/0.72 (step t933.t14 (cl (= tptp.n tptp.m)) :rule trans :premises (t933.t12 t933.t13))
% 0.55/0.72 (step t933.t15 (cl (= (= tptp.n tptp.m) true)) :rule resolution :premises (t933.t10 t933.t14))
% 0.55/0.72 (step t933.t16 (cl (= false true)) :rule trans :premises (t933.t8 t933.t15))
% 0.55/0.72 (step t933.t17 (cl false) :rule resolution :premises (t933.t1 t933.t2 t933.t16))
% 0.55/0.72 (step t933 (cl (not (= tptp.n tptp.k)) (not (= tptp.m tptp.k)) (not (not (= tptp.n tptp.m))) false) :rule subproof :discharge (t933.a0 t933.a1 t933.a2))
% 0.55/0.72 (step t934 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t935 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t936 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (= tptp.n tptp.m))) :rule and_pos)
% 0.55/0.72 (step t937 (cl false (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule resolution :premises (t933 t934 t935 t936))
% 0.55/0.72 (step t938 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) false) :rule reordering :premises (t937))
% 0.55/0.72 (step t939 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) false) :rule contraction :premises (t938))
% 0.55/0.72 (step t940 (cl (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) false) :rule resolution :premises (t932 t939))
% 0.55/0.72 (step t941 (cl (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (not false)) :rule implies_neg2)
% 0.55/0.72 (step t942 (cl (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false)) :rule resolution :premises (t940 t941))
% 0.55/0.72 (step t943 (cl (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false)) :rule contraction :premises (t942))
% 0.55/0.72 (step t944 (cl (= (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))))) :rule implies_simplify)
% 0.55/0.72 (step t945 (cl (not (=> (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false)) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule equiv1 :premises (t944))
% 0.55/0.72 (step t946 (cl (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule resolution :premises (t943 t945))
% 0.55/0.72 (step t947 (cl (= (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) false)) :rule resolution :premises (t931 t946))
% 0.55/0.72 (step t948 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) false))) :rule cong :premises (t927 t947))
% 0.55/0.72 (step t949 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) false) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))))) :rule all_simplify)
% 0.55/0.72 (step t950 (cl (= (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))))) :rule trans :premises (t948 t949))
% 0.55/0.72 (step t951 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t952)
% 0.55/0.72 (assume t952.a0 (not (= tptp.n tptp.m)))
% 0.55/0.72 (assume t952.a1 (= tptp.m tptp.k))
% 0.55/0.72 (assume t952.a2 (= tptp.n tptp.k))
% 0.55/0.72 (step t952.t1 (cl (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) (not (= tptp.n tptp.k)) (not (= tptp.m tptp.k)) (not (not (= tptp.n tptp.m)))) :rule and_neg)
% 0.55/0.72 (step t952.t2 (cl (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule resolution :premises (t952.t1 t952.a2 t952.a1 t952.a0))
% 0.55/0.72 (step t952 (cl (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule subproof :discharge (t952.a0 t952.a1 t952.a2))
% 0.55/0.72 (step t953 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (not (= tptp.n tptp.m))) :rule and_pos)
% 0.55/0.72 (step t954 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (= tptp.m tptp.k)) :rule and_pos)
% 0.55/0.72 (step t955 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t956 (cl (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)))) :rule resolution :premises (t952 t953 t954 t955))
% 0.55/0.72 (step t957 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule reordering :premises (t956))
% 0.55/0.72 (step t958 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k))) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule contraction :premises (t957))
% 0.55/0.72 (step t959 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) :rule resolution :premises (t951 t958))
% 0.55/0.72 (step t960 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (not (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule implies_neg2)
% 0.55/0.72 (step t961 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m)))) (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule resolution :premises (t959 t960))
% 0.55/0.72 (step t962 (cl (=> (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)) (and (= tptp.n tptp.k) (= tptp.m tptp.k) (not (= tptp.n tptp.m))))) :rule contraction :premises (t961))
% 0.55/0.72 (step t963 (cl (not (and (not (= tptp.n tptp.m)) (= tptp.m tptp.k) (= tptp.n tptp.k)))) :rule resolution :premises (t926 t950 t962))
% 0.55/0.72 (step t964 (cl (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) :rule not_and :premises (t963))
% 0.55/0.72 (step t965 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (not (not (not (= tptp.n tptp.m))))) :rule or_neg)
% 0.55/0.72 (step t966 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (not (not (= tptp.m tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t967 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t968 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)))) :rule resolution :premises (t964 t965 t966 t967))
% 0.55/0.72 (step t969 (cl (or (not (not (= tptp.n tptp.m))) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)))) :rule contraction :premises (t968))
% 0.55/0.72 (step t970 (cl (or (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k)))) :rule resolution :premises (t924 t925 t969))
% 0.55/0.72 (step t971 (cl (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) :rule or :premises (t970))
% 0.55/0.72 (step t972 (cl (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k)) (not (= tptp.n tptp.k))) :rule resolution :premises (t923 t971 t891))
% 0.55/0.72 (step t973 (cl (not (= tptp.j tptp.k)) (not (= tptp.n tptp.k))) :rule contraction :premises (t972))
% 0.55/0.72 (step t974 (cl (not (= tptp.j tptp.k)) (not (= tptp.j tptp.k))) :rule resolution :premises (t830 t973))
% 0.55/0.72 (step t975 (cl (not (= tptp.j tptp.k))) :rule contraction :premises (t974))
% 0.55/0.72 (step t976 (cl (= tptp.n tptp.m) (not (= tptp.m tptp.k)) (not (= tptp.n tptp.k))) :rule or :premises (t970))
% 0.55/0.72 (step t977 (cl (not (= tptp.n tptp.m))) :rule not_symm :premises (a0))
% 0.55/0.72 (step t978 (cl (not (= tptp.m tptp.k))) :rule resolution :premises (t976 t977 t622))
% 0.55/0.72 (step t979 (cl (not (= (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (= tptp.n tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (= tptp.n (tptp.f tptp.k)))))) (not (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k))))) (or (not (= tptp.n tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (= tptp.n (tptp.f tptp.k))))) :rule equiv_pos2)
% 0.55/0.72 (step t980 (cl (= (= (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k))) true) (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k))))) :rule equiv_simplify)
% 0.55/0.72 (step t981 (cl (not (= (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k))) true)) (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k)))) :rule equiv1 :premises (t980))
% 0.55/0.72 (step t982 (cl (= (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k))) (= (= tptp.k (tptp.f tptp.k)) (not (not (= tptp.k (tptp.f tptp.k))))))) :rule all_simplify)
% 0.55/0.72 (step t983 (cl (= (= tptp.k (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k)))) :rule refl)
% 0.55/0.72 (step t984 (cl (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k)))) :rule all_simplify)
% 0.55/0.72 (step t985 (cl (= (= (= tptp.k (tptp.f tptp.k)) (not (not (= tptp.k (tptp.f tptp.k))))) (= (= tptp.k (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k))))) :rule cong :premises (t983 t984))
% 0.55/0.72 (step t986 (cl (= (= (= tptp.k (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k))) true)) :rule all_simplify)
% 0.55/0.72 (step t987 (cl (= (= (= tptp.k (tptp.f tptp.k)) (not (not (= tptp.k (tptp.f tptp.k))))) true)) :rule trans :premises (t985 t986))
% 0.55/0.72 (step t988 (cl (= (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k))) true)) :rule trans :premises (t982 t987))
% 0.55/0.72 (step t989 (cl (= (not (not (= tptp.k (tptp.f tptp.k)))) (= tptp.k (tptp.f tptp.k)))) :rule resolution :premises (t981 t988))
% 0.55/0.72 (step t990 (cl (= (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (= tptp.n tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (= tptp.n (tptp.f tptp.k)))))) :rule cong :premises (t2 t989 t114))
% 0.55/0.72 (step t991 (cl (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k))))) :rule and_neg)
% 0.55/0.72 (step t992 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t993)
% 0.55/0.72 (assume t993.a0 (= tptp.n tptp.k))
% 0.55/0.72 (assume t993.a1 (not (= tptp.k (tptp.f tptp.k))))
% 0.55/0.72 (step t993.t1 (cl (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t993.t2)
% 0.55/0.72 (assume t993.t2.a0 (not (= tptp.k (tptp.f tptp.k))))
% 0.55/0.72 (assume t993.t2.a1 (= tptp.n tptp.k))
% 0.55/0.72 (step t993.t2.t1 (cl (= (= (= tptp.n (tptp.f tptp.k)) false) (not (= tptp.n (tptp.f tptp.k))))) :rule equiv_simplify)
% 0.55/0.72 (step t993.t2.t2 (cl (not (= (= tptp.n (tptp.f tptp.k)) false)) (not (= tptp.n (tptp.f tptp.k)))) :rule equiv1 :premises (t993.t2.t1))
% 0.55/0.72 (step t993.t2.t3 (cl (= tptp.k tptp.n)) :rule symm :premises (t993.t2.a1))
% 0.55/0.72 (step t993.t2.t4 (cl (= tptp.n tptp.k)) :rule symm :premises (t993.t2.t3))
% 0.55/0.72 (step t993.t2.t5 (cl (= (tptp.f tptp.k) (tptp.f tptp.k))) :rule refl)
% 0.55/0.72 (step t993.t2.t6 (cl (= (= tptp.n (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k)))) :rule cong :premises (t993.t2.t4 t993.t2.t5))
% 0.55/0.72 (step t993.t2.t7 (cl (= (= (= tptp.k (tptp.f tptp.k)) false) (not (= tptp.k (tptp.f tptp.k))))) :rule equiv_simplify)
% 0.55/0.72 (step t993.t2.t8 (cl (= (= tptp.k (tptp.f tptp.k)) false) (not (not (= tptp.k (tptp.f tptp.k))))) :rule equiv2 :premises (t993.t2.t7))
% 0.55/0.72 (step t993.t2.t9 (cl (not (not (not (= tptp.k (tptp.f tptp.k))))) (= tptp.k (tptp.f tptp.k))) :rule not_not)
% 0.55/0.72 (step t993.t2.t10 (cl (= (= tptp.k (tptp.f tptp.k)) false) (= tptp.k (tptp.f tptp.k))) :rule resolution :premises (t993.t2.t8 t993.t2.t9))
% 0.55/0.72 (step t993.t2.t11 (cl (= (= tptp.k (tptp.f tptp.k)) false)) :rule resolution :premises (t993.t2.t10 t993.t2.a0))
% 0.55/0.72 (step t993.t2.t12 (cl (= (= tptp.n (tptp.f tptp.k)) false)) :rule trans :premises (t993.t2.t6 t993.t2.t11))
% 0.55/0.72 (step t993.t2.t13 (cl (not (= tptp.n (tptp.f tptp.k)))) :rule resolution :premises (t993.t2.t2 t993.t2.t12))
% 0.55/0.72 (step t993.t2 (cl (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) :rule subproof :discharge (t993.t2.a0 t993.t2.a1))
% 0.55/0.72 (step t993.t3 (cl (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (= tptp.k (tptp.f tptp.k)))) :rule and_pos)
% 0.55/0.72 (step t993.t4 (cl (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t993.t5 (cl (not (= tptp.n (tptp.f tptp.k))) (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)))) :rule resolution :premises (t993.t2 t993.t3 t993.t4))
% 0.55/0.72 (step t993.t6 (cl (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) :rule reordering :premises (t993.t5))
% 0.55/0.72 (step t993.t7 (cl (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) :rule contraction :premises (t993.t6))
% 0.55/0.72 (step t993.t8 (cl (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) :rule resolution :premises (t993.t1 t993.t7))
% 0.55/0.72 (step t993.t9 (cl (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) (not (not (= tptp.n (tptp.f tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t993.t10 (cl (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t993.t8 t993.t9))
% 0.55/0.72 (step t993.t11 (cl (=> (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (= tptp.n (tptp.f tptp.k))))) :rule contraction :premises (t993.t10))
% 0.55/0.72 (step t993.t12 (cl (not (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) (not (= tptp.n (tptp.f tptp.k)))) :rule implies :premises (t993.t11))
% 0.55/0.72 (step t993.t13 (cl (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n tptp.k))) :rule and_neg)
% 0.55/0.72 (step t993.t14 (cl (and (not (= tptp.k (tptp.f tptp.k))) (= tptp.n tptp.k))) :rule resolution :premises (t993.t13 t993.a1 t993.a0))
% 0.55/0.72 (step t993.t15 (cl (not (= tptp.n (tptp.f tptp.k)))) :rule resolution :premises (t993.t12 t993.t14))
% 0.55/0.72 (step t993 (cl (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) :rule subproof :discharge (t993.a0 t993.a1))
% 0.55/0.72 (step t994 (cl (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (= tptp.n tptp.k)) :rule and_pos)
% 0.55/0.72 (step t995 (cl (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (= tptp.k (tptp.f tptp.k)))) :rule and_pos)
% 0.55/0.72 (step t996 (cl (not (= tptp.n (tptp.f tptp.k))) (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))))) :rule resolution :premises (t993 t994 t995))
% 0.55/0.72 (step t997 (cl (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (= tptp.n (tptp.f tptp.k)))) :rule reordering :premises (t996))
% 0.55/0.72 (step t998 (cl (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (= tptp.n (tptp.f tptp.k)))) :rule contraction :premises (t997))
% 0.55/0.72 (step t999 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) :rule resolution :premises (t992 t998))
% 0.55/0.72 (step t1000 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (= tptp.n (tptp.f tptp.k))))) :rule implies_neg2)
% 0.55/0.72 (step t1001 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t999 t1000))
% 0.55/0.72 (step t1002 (cl (=> (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k))))) :rule contraction :premises (t1001))
% 0.55/0.72 (step t1003 (cl (not (and (= tptp.n tptp.k) (not (= tptp.k (tptp.f tptp.k))))) (not (= tptp.n (tptp.f tptp.k)))) :rule implies :premises (t1002))
% 0.55/0.72 (step t1004 (cl (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) :rule resolution :premises (t991 t1003))
% 0.55/0.72 (step t1005 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (= tptp.n tptp.k)))) :rule or_neg)
% 0.55/0.72 (step t1006 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (not (= tptp.k (tptp.f tptp.k)))))) :rule or_neg)
% 0.55/0.72 (step t1007 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (not (not (= tptp.n (tptp.f tptp.k))))) :rule or_neg)
% 0.55/0.72 (step t1008 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k)))) (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t1004 t1005 t1006 t1007))
% 0.55/0.72 (step t1009 (cl (or (not (= tptp.n tptp.k)) (not (not (= tptp.k (tptp.f tptp.k)))) (not (= tptp.n (tptp.f tptp.k))))) :rule contraction :premises (t1008))
% 0.55/0.72 (step t1010 (cl (or (not (= tptp.n tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (= tptp.n (tptp.f tptp.k))))) :rule resolution :premises (t979 t990 t1009))
% 0.55/0.72 (step t1011 (cl (not (= tptp.n tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (= tptp.n (tptp.f tptp.k)))) :rule or :premises (t1010))
% 0.55/0.72 (step t1012 (cl (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (= tptp.k (tptp.f tptp.k)) (not (tptp.element tptp.k tptp.m))) :rule resolution :premises (t1011 t622 t163 t174 t176 t187 t978))
% 0.55/0.72 (step t1013 (cl (= tptp.k (tptp.f tptp.k)) (= tptp.m (tptp.f tptp.k)) (not (tptp.element tptp.k tptp.m))) :rule contraction :premises (t1012))
% 0.55/0.72 (step t1014 (cl (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.k tptp.m)) (not (tptp.element tptp.k tptp.m))) :rule resolution :premises (t1013 t202 t213 t978 t215 t226 t978))
% 0.55/0.72 (step t1015 (cl (not (tptp.element tptp.k tptp.m))) :rule contraction :premises (t1014))
% 0.55/0.72 (step t1016 (cl (not (tptp.element tptp.j tptp.k))) :rule resolution :premises (t760 t975 t978 t1015))
% 0.55/0.72 (step t1017 (cl (not (tptp.element tptp.j tptp.n))) :rule resolution :premises (t669 t622 t1016))
% 0.55/0.72 (step t1018 (cl (not (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))) :rule or_pos)
% 0.55/0.72 (step t1019 (cl (= tptp.j (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))))) :rule reordering :premises (t1018))
% 0.55/0.72 (step t1020 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t1021)
% 0.55/0.72 (assume t1021.a0 (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))))
% 0.55/0.72 (step t1021.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))))) :rule forall_inst :args ((:= Y (tptp.g tptp.j))))
% 0.55/0.72 (step t1021.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule or :premises (t1021.t1))
% 0.55/0.72 (step t1021.t3 (cl (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule resolution :premises (t1021.t2 t1021.a0))
% 0.55/0.72 (step t1021 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule subproof :discharge (t1021.a0))
% 0.55/0.72 (step t1022 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule resolution :premises (t1020 t1021))
% 0.55/0.72 (step t1023 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) (not (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))))) :rule implies_neg2)
% 0.55/0.72 (step t1024 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))))) :rule resolution :premises (t1022 t1023))
% 0.55/0.72 (step t1025 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j)))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j))))) :rule contraction :premises (t1024))
% 0.55/0.72 (step t1026 (cl (not (forall ((Y $$unsorted)) (or (= tptp.j Y) (= tptp.k Y) (not (tptp.element Y tptp.j))))) (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule implies :premises (t1025))
% 0.55/0.72 (step t1027 (cl (or (= tptp.j (tptp.g tptp.j)) (= tptp.k (tptp.g tptp.j)) (not (tptp.element (tptp.g tptp.j) tptp.j)))) :rule resolution :premises (t1026 t793))
% 0.55/0.72 (step t1028 (cl (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)) :rule or_pos)
% 0.55/0.72 (step t1029 (cl (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)))) :rule reordering :premises (t1028))
% 0.55/0.72 (step t1030 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t1031)
% 0.55/0.72 (assume t1031.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))))
% 0.55/0.72 (step t1031.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)))) :rule forall_inst :args ((:= Y tptp.j)))
% 0.55/0.72 (step t1031.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule or :premises (t1031.t1))
% 0.55/0.72 (step t1031.t3 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule resolution :premises (t1031.t2 t1031.a0))
% 0.55/0.72 (step t1031 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule subproof :discharge (t1031.a0))
% 0.55/0.72 (step t1032 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule resolution :premises (t1030 t1031))
% 0.55/0.72 (step t1033 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)))) :rule implies_neg2)
% 0.55/0.72 (step t1034 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)))) :rule resolution :premises (t1032 t1033))
% 0.55/0.72 (step t1035 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j)))) :rule contraction :premises (t1034))
% 0.55/0.72 (step t1036 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (tptp.element (tptp.g Y) Y)))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule implies :premises (t1035))
% 0.55/0.72 (step t1037 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (tptp.element (tptp.g tptp.j) tptp.j))) :rule resolution :premises (t1036 t316))
% 0.55/0.72 (step t1038 (cl (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))) :rule or_pos)
% 0.55/0.72 (step t1039 (cl (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))))) :rule reordering :premises (t1038))
% 0.55/0.72 (step t1040 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) :rule implies_neg1)
% 0.55/0.72 (anchor :step t1041)
% 0.55/0.72 (assume t1041.a0 (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))))
% 0.55/0.72 (step t1041.t1 (cl (or (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))))) :rule forall_inst :args ((:= Y tptp.j)))
% 0.55/0.72 (step t1041.t2 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule or :premises (t1041.t1))
% 0.55/0.72 (step t1041.t3 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule resolution :premises (t1041.t2 t1041.a0))
% 0.55/0.72 (step t1041 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule subproof :discharge (t1041.a0))
% 0.55/0.72 (step t1042 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule resolution :premises (t1040 t1041))
% 0.55/0.72 (step t1043 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) (not (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))))) :rule implies_neg2)
% 0.55/0.72 (step t1044 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))))) :rule resolution :premises (t1042 t1043))
% 0.55/0.72 (step t1045 (cl (=> (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j)))))) :rule contraction :premises (t1044))
% 0.55/0.72 (step t1046 (cl (not (forall ((Y $$unsorted)) (or (= tptp.n Y) (tptp.element Y tptp.n) (not (= Y (tptp.g Y)))))) (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule implies :premises (t1045))
% 0.55/0.72 (step t1047 (cl (or (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (not (= tptp.j (tptp.g tptp.j))))) :rule resolution :premises (t1046 t344))
% 0.55/0.72 (step t1048 (cl (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n)) :rule resolution :premises (t1019 t1027 t1029 t1037 t1039 t1047))
% 0.55/0.72 (step t1049 (cl (= tptp.k (tptp.g tptp.j)) (= tptp.n tptp.j) (tptp.element tptp.j tptp.n)) :rule contraction :premises (t1048))
% 0.55/0.72 (step t1050 (cl (= tptp.n tptp.j) (tptp.element tptp.j tptp.n) (= tptp.k (tptp.g tptp.j))) :rule reordering :premises (t1049))
% 0.55/0.72 (step t1051 (cl (= tptp.n tptp.j) (= tptp.n tptp.j)) :rule resolution :premises (t76 t622 t624 t635 t1017 t1050 t1017))
% 0.55/0.72 (step t1052 (cl (= tptp.n tptp.j)) :rule contraction :premises (t1051))
% 0.55/0.72 (step t1053 (cl) :rule resolution :premises (t61 t1052 t622 t975))
% 0.55/0.72
% 0.55/0.72 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.Ach58sijBq/cvc5---1.0.5_27963.smt2
% 0.55/0.72 % cvc5---1.0.5 exiting
% 0.55/0.73 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------