TSTP Solution File: SEV282^5 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:58:08 EDT 2024
% Result : Theorem 0.22s 0.52s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 13:05:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.52 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.Pv4i7G7w5O/cvc5---1.0.5_4851.smt2
% 0.22/0.52 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.Pv4i7G7w5O/cvc5---1.0.5_4851.smt2
% 0.22/0.52 (assume a0 (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))))
% 0.22/0.52 (assume a1 (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))))
% 0.22/0.52 (assume a2 (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))))
% 0.22/0.52 (assume a3 (not (@ tptp.cNAT tptp.cZERO)))
% 0.22/0.52 (assume a4 true)
% 0.22/0.52 (step t1 (cl (not (= (not (@ tptp.cNAT tptp.cZERO)) false)) (not (not (@ tptp.cNAT tptp.cZERO))) false) :rule equiv_pos2)
% 0.22/0.52 (step t2 (cl (and (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))))) (not (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) (not (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule and_neg)
% 0.22/0.52 (step t3 (cl (not (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))))) (not (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))))) :rule equiv_pos2)
% 0.22/0.52 (step t4 (cl (= tptp.cNAT tptp.cNAT)) :rule refl)
% 0.22/0.52 (anchor :step t5 :args ((Xn (-> (-> $$unsorted Bool) Bool)) (:= Xn Xn)))
% 0.22/0.52 (step t5.t1 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (anchor :step t5.t2 :args ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t5.t2.t1 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t5.t2.t2 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t5.t2.t3 (cl (and (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) (not (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule and_neg)
% 0.22/0.52 (step t5.t2.t4 (cl (not (= (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))) (not (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule equiv_pos2)
% 0.22/0.52 (step t5.t2.t5 (cl (= tptp.cSUCC tptp.cSUCC)) :rule refl)
% 0.22/0.52 (anchor :step t5.t2.t6 :args ((Xn (-> (-> $$unsorted Bool) Bool)) (:= Xn Xn) (Xp (-> $$unsorted Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t5.t2.t6.t1 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (step t5.t2.t6.t2 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (anchor :step t5.t2.t6.t3 :args ((Xx $$unsorted) (:= Xx Xx)))
% 0.22/0.52 (step t5.t2.t6.t3.t1 (cl (= Xx Xx)) :rule refl)
% 0.22/0.52 (step t5.t2.t6.t3.t2 (cl (= (@ Xp Xx) (@ Xp Xx))) :rule refl)
% 0.22/0.52 (step t5.t2.t6.t3.t3 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (anchor :step t5.t2.t6.t3.t4 :args ((Xt $$unsorted) (:= Xt Xt)))
% 0.22/0.52 (step t5.t2.t6.t3.t4.t1 (cl (= Xt Xt)) :rule refl)
% 0.22/0.52 (step t5.t2.t6.t3.t4.t2 (cl (= (= Xt Xx) (= Xx Xt))) :rule all_simplify)
% 0.22/0.52 (step t5.t2.t6.t3.t4.t3 (cl (= (not (= Xt Xx)) (not (= Xx Xt)))) :rule cong :premises (t5.t2.t6.t3.t4.t2))
% 0.22/0.52 (step t5.t2.t6.t3.t4.t4 (cl (= (@ Xp Xt) (@ Xp Xt))) :rule refl)
% 0.22/0.52 (step t5.t2.t6.t3.t4.t5 (cl (= (and (not (= Xt Xx)) (@ Xp Xt)) (and (not (= Xx Xt)) (@ Xp Xt)))) :rule cong :premises (t5.t2.t6.t3.t4.t3 t5.t2.t6.t3.t4.t4))
% 0.22/0.52 (step t5.t2.t6.t3.t4 (cl (= (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))) (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))) :rule bind)
% 0.22/0.52 (step t5.t2.t6.t3.t5 (cl (= (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) :rule cong :premises (t5.t2.t6.t3.t3 t5.t2.t6.t3.t4))
% 0.22/0.52 (step t5.t2.t6.t3.t6 (cl (= (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))) :rule cong :premises (t5.t2.t6.t3.t2 t5.t2.t6.t3.t5))
% 0.22/0.52 (step t5.t2.t6.t3 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))) :rule bind)
% 0.22/0.52 (step t5.t2.t6.t4 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule all_simplify)
% 0.22/0.52 (step t5.t2.t6.t5 (cl (= (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))) (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) :rule all_simplify)
% 0.22/0.52 (step t5.t2.t6.t6 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule cong :premises (t5.t2.t6.t5))
% 0.22/0.52 (step t5.t2.t6.t7 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule trans :premises (t5.t2.t6.t4 t5.t2.t6.t6))
% 0.22/0.52 (step t5.t2.t6.t8 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule trans :premises (t5.t2.t6.t3 t5.t2.t6.t7))
% 0.22/0.52 (step t5.t2.t6 (cl (= (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))))) (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule bind)
% 0.22/0.52 (step t5.t2.t7 (cl (= (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))) :rule cong :premises (t5.t2.t5 t5.t2.t6))
% 0.22/0.52 (step t5.t2.t8 (cl (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule resolution :premises (t5.t2.t4 t5.t2.t7 a1))
% 0.22/0.52 (step t5.t2.t9 (cl (not (= (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) (not (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx)))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule equiv_pos2)
% 0.22/0.52 (step t5.t2.t10 (cl (= tptp.cZERO tptp.cZERO)) :rule refl)
% 0.22/0.52 (anchor :step t5.t2.t11 :args ((Xp (-> $$unsorted Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t5.t2.t11.t1 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t5.t2.t11.t2 (cl (= (exists ((Xx $$unsorted)) (@ Xp Xx)) (not (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule all_simplify)
% 0.22/0.52 (step t5.t2.t11.t3 (cl (= (not (exists ((Xx $$unsorted)) (@ Xp Xx))) (not (not (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t5.t2.t11.t2))
% 0.22/0.52 (step t5.t2.t11.t4 (cl (= (not (not (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) :rule all_simplify)
% 0.22/0.52 (step t5.t2.t11.t5 (cl (= (not (exists ((Xx $$unsorted)) (@ Xp Xx))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) :rule trans :premises (t5.t2.t11.t3 t5.t2.t11.t4))
% 0.22/0.52 (step t5.t2.t11 (cl (= (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule bind)
% 0.22/0.52 (step t5.t2.t12 (cl (= (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t5.t2.t10 t5.t2.t11))
% 0.22/0.52 (step t5.t2.t13 (cl (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule resolution :premises (t5.t2.t9 t5.t2.t12 a0))
% 0.22/0.52 (step t5.t2.t14 (cl (and (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule resolution :premises (t5.t2.t3 t5.t2.t8 t5.t2.t13))
% 0.22/0.52 (step t5.t2.t15 (cl (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule and :premises (t5.t2.t14))
% 0.22/0.52 (step t5.t2.t16 (cl (= (@ Xp tptp.cZERO) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t5.t2.t2 t5.t2.t15))
% 0.22/0.52 (step t5.t2.t17 (cl (= (not (@ Xp tptp.cZERO)) (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))))) :rule cong :premises (t5.t2.t16))
% 0.22/0.52 (anchor :step t5.t2.t18 :args ((Xx (-> (-> $$unsorted Bool) Bool)) (:= Xx Xx)))
% 0.22/0.52 (step t5.t2.t18.t1 (cl (= Xx Xx)) :rule refl)
% 0.22/0.52 (step t5.t2.t18.t2 (cl (= (not (@ Xp Xx)) (not (@ Xp Xx)))) :rule refl)
% 0.22/0.52 (step t5.t2.t18.t3 (cl (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule and :premises (t5.t2.t14))
% 0.22/0.52 (step t5.t2.t18.t4 (cl (= Xx Xx)) :rule refl)
% 0.22/0.52 (step t5.t2.t18.t5 (cl (= (@ tptp.cSUCC Xx) (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))) :rule cong :premises (t5.t2.t18.t3 t5.t2.t18.t4))
% 0.22/0.52 (step t5.t2.t18.t6 (cl (= (@ Xp (@ tptp.cSUCC Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx)))) :rule cong :premises (t5.t2.t2 t5.t2.t18.t5))
% 0.22/0.52 (step t5.t2.t18.t7 (cl (= (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) :rule cong :premises (t5.t2.t18.t2 t5.t2.t18.t6))
% 0.22/0.52 (step t5.t2.t18 (cl (= (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx)))) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx)))))) :rule bind)
% 0.22/0.52 (step t5.t2.t19 (cl (= (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))))) :rule cong :premises (t5.t2.t18))
% 0.22/0.52 (step t5.t2.t20 (cl (= (@ Xp Xn) (@ Xp Xn))) :rule refl)
% 0.22/0.52 (step t5.t2.t21 (cl (= (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn)))) :rule cong :premises (t5.t2.t17 t5.t2.t19 t5.t2.t20))
% 0.22/0.52 (step t5.t2 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn))))) :rule bind)
% 0.22/0.52 (step t5 (cl (= (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))) (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn)))))) :rule bind)
% 0.22/0.52 (step t6 (cl (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn))))))) :rule cong :premises (t4 t5))
% 0.22/0.52 (step t7 (cl (= tptp.cNAT tptp.cNAT)) :rule refl)
% 0.22/0.52 (anchor :step t8 :args ((Xn (-> (-> $$unsorted Bool) Bool)) (:= Xn Xn)))
% 0.22/0.52 (step t8.t1 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (anchor :step t8.t2 :args ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t8.t2.t1 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t8.t2.t2 (cl (= (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))))) :rule refl)
% 0.22/0.52 (anchor :step t8.t2.t3 :args ((Xx (-> (-> $$unsorted Bool) Bool)) (:= Xx Xx)))
% 0.22/0.52 (step t8.t2.t3.t1 (cl (= Xx Xx)) :rule refl)
% 0.22/0.52 (step t8.t2.t3.t2 (cl (= (not (@ Xp Xx)) (not (@ Xp Xx)))) :rule refl)
% 0.22/0.52 (step t8.t2.t3.t3 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t8.t2.t3.t4 (cl (= (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx) (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule all_simplify)
% 0.22/0.52 (step t8.t2.t3.t5 (cl (= (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))) :rule cong :premises (t8.t2.t3.t3 t8.t2.t3.t4))
% 0.22/0.52 (step t8.t2.t3.t6 (cl (= (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) :rule cong :premises (t8.t2.t3.t2 t8.t2.t3.t5))
% 0.22/0.52 (step t8.t2.t3 (cl (= (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx)))) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))))) :rule bind)
% 0.22/0.52 (step t8.t2.t4 (cl (= (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))))) :rule cong :premises (t8.t2.t3))
% 0.22/0.52 (step t8.t2.t5 (cl (= (@ Xp Xn) (@ Xp Xn))) :rule refl)
% 0.22/0.52 (step t8.t2.t6 (cl (= (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn)) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) :rule cong :premises (t8.t2.t2 t8.t2.t4 t8.t2.t5))
% 0.22/0.52 (step t8.t2 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))) :rule bind)
% 0.22/0.52 (step t8 (cl (= (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn)))) (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))))) :rule bind)
% 0.22/0.52 (step t9 (cl (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))))) :rule cong :premises (t7 t8))
% 0.22/0.52 (step t10 (cl (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))))) :rule trans :premises (t6 t9))
% 0.22/0.52 (step t11 (cl (not (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))))) (not (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))))) :rule equiv_pos2)
% 0.22/0.52 (anchor :step t12 :args ((Xn (-> (-> $$unsorted Bool) Bool)) (:= Xn Xn)))
% 0.22/0.52 (step t12.t1 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (anchor :step t12.t2 :args ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t12.t2.t1 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t12.t2.t2 (cl (= (@ Xp tptp.cZERO) (@ Xp tptp.cZERO))) :rule refl)
% 0.22/0.52 (step t12.t2.t3 (cl (= (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx)))) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx)))))) :rule all_simplify)
% 0.22/0.52 (step t12.t2.t4 (cl (= (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))))) :rule cong :premises (t12.t2.t2 t12.t2.t3))
% 0.22/0.52 (step t12.t2.t5 (cl (= (@ Xp Xn) (@ Xp Xn))) :rule refl)
% 0.22/0.52 (step t12.t2.t6 (cl (= (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))) :rule cong :premises (t12.t2.t4 t12.t2.t5))
% 0.22/0.52 (step t12.t2 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) :rule bind)
% 0.22/0.52 (step t12.t3 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) :rule all_simplify)
% 0.22/0.52 (step t12.t4 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) :rule trans :premises (t12.t2 t12.t3))
% 0.22/0.52 (step t12 (cl (= (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))) (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))))) :rule bind)
% 0.22/0.52 (step t13 (cl (= (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))))) :rule cong :premises (t7 t12))
% 0.22/0.52 (step t14 (cl (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn)))))) :rule resolution :premises (t11 t13 a2))
% 0.22/0.52 (step t15 (cl (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))))) :rule resolution :premises (t3 t10 t14))
% 0.22/0.52 (step t16 (cl (not (= (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))) (not (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule equiv_pos2)
% 0.22/0.52 (step t17 (cl (= tptp.cSUCC tptp.cSUCC)) :rule refl)
% 0.22/0.52 (anchor :step t18 :args ((Xn (-> (-> $$unsorted Bool) Bool)) (:= Xn Xn) (Xp (-> $$unsorted Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t18.t1 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (step t18.t2 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (anchor :step t18.t3 :args ((Xx $$unsorted) (:= Xx Xx)))
% 0.22/0.52 (step t18.t3.t1 (cl (= Xx Xx)) :rule refl)
% 0.22/0.52 (step t18.t3.t2 (cl (= (@ Xp Xx) (@ Xp Xx))) :rule refl)
% 0.22/0.52 (step t18.t3.t3 (cl (= Xn Xn)) :rule refl)
% 0.22/0.52 (anchor :step t18.t3.t4 :args ((Xt $$unsorted) (:= Xt Xt)))
% 0.22/0.52 (step t18.t3.t4.t1 (cl (= Xt Xt)) :rule refl)
% 0.22/0.52 (step t18.t3.t4.t2 (cl (= (= Xt Xx) (= Xx Xt))) :rule all_simplify)
% 0.22/0.52 (step t18.t3.t4.t3 (cl (= (not (= Xt Xx)) (not (= Xx Xt)))) :rule cong :premises (t18.t3.t4.t2))
% 0.22/0.52 (step t18.t3.t4.t4 (cl (= (@ Xp Xt) (@ Xp Xt))) :rule refl)
% 0.22/0.52 (step t18.t3.t4.t5 (cl (= (and (not (= Xt Xx)) (@ Xp Xt)) (and (not (= Xx Xt)) (@ Xp Xt)))) :rule cong :premises (t18.t3.t4.t3 t18.t3.t4.t4))
% 0.22/0.52 (step t18.t3.t4 (cl (= (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))) (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))) :rule bind)
% 0.22/0.52 (step t18.t3.t5 (cl (= (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) :rule cong :premises (t18.t3.t3 t18.t3.t4))
% 0.22/0.52 (step t18.t3.t6 (cl (= (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))) :rule cong :premises (t18.t3.t2 t18.t3.t5))
% 0.22/0.52 (step t18.t3 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))) :rule bind)
% 0.22/0.52 (step t18.t4 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule all_simplify)
% 0.22/0.52 (step t18.t5 (cl (= (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))) (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))) :rule all_simplify)
% 0.22/0.52 (step t18.t6 (cl (= (not (forall ((Xx $$unsorted)) (not (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule cong :premises (t18.t5))
% 0.22/0.52 (step t18.t7 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule trans :premises (t18.t4 t18.t6))
% 0.22/0.52 (step t18.t8 (cl (= (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) :rule trans :premises (t18.t3 t18.t7))
% 0.22/0.52 (step t18 (cl (= (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt))))))) (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule bind)
% 0.22/0.52 (step t19 (cl (= (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))))) :rule cong :premises (t17 t18))
% 0.22/0.52 (step t20 (cl (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))) :rule resolution :premises (t16 t19 a1))
% 0.22/0.52 (step t21 (cl (not (= (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) (not (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx)))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule equiv_pos2)
% 0.22/0.52 (step t22 (cl (= tptp.cZERO tptp.cZERO)) :rule refl)
% 0.22/0.52 (anchor :step t23 :args ((Xp (-> $$unsorted Bool)) (:= Xp Xp)))
% 0.22/0.52 (step t23.t1 (cl (= Xp Xp)) :rule refl)
% 0.22/0.52 (step t23.t2 (cl (= (exists ((Xx $$unsorted)) (@ Xp Xx)) (not (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule all_simplify)
% 0.22/0.52 (step t23.t3 (cl (= (not (exists ((Xx $$unsorted)) (@ Xp Xx))) (not (not (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t23.t2))
% 0.22/0.52 (step t23.t4 (cl (= (not (not (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) :rule all_simplify)
% 0.22/0.52 (step t23.t5 (cl (= (not (exists ((Xx $$unsorted)) (@ Xp Xx))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) :rule trans :premises (t23.t3 t23.t4))
% 0.22/0.52 (step t23 (cl (= (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule bind)
% 0.22/0.52 (step t24 (cl (= (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t22 t23))
% 0.22/0.52 (step t25 (cl (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule resolution :premises (t21 t24 a0))
% 0.22/0.52 (step t26 (cl (and (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn))))) (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt)))))))))) (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule resolution :premises (t2 t15 t20 t25))
% 0.22/0.52 (step t27 (cl (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))))) :rule and :premises (t26))
% 0.22/0.52 (step t28 (cl (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) :rule and :premises (t26))
% 0.22/0.52 (step t29 (cl (= (@ tptp.cNAT tptp.cZERO) (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) :rule cong :premises (t27 t28))
% 0.22/0.52 (step t30 (cl (= (not (@ tptp.cNAT tptp.cZERO)) (not (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))))) :rule cong :premises (t29))
% 0.22/0.52 (step t31 (cl (= (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))))) :rule all_simplify)
% 0.22/0.52 (step t32 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) true))) :rule all_simplify)
% 0.22/0.52 (step t33 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) true) true)) :rule all_simplify)
% 0.22/0.52 (step t34 (cl (= (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))))) true)) :rule trans :premises (t32 t33))
% 0.22/0.52 (step t35 (cl (= (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx))))) true)) :rule trans :premises (t31 t34))
% 0.22/0.52 (step t36 (cl (= (not (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not true))) :rule cong :premises (t35))
% 0.22/0.52 (step t37 (cl (= (not true) false)) :rule all_simplify)
% 0.22/0.52 (step t38 (cl (= (not (@ (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (lambda ((Xp (-> $$unsorted Bool))) (not (forall ((Xx $$unsorted)) (or (not (@ Xp Xx)) (not (@ Xx (lambda ((Xt $$unsorted)) (and (not (= Xx Xt)) (@ Xp Xt))))))))))))) (@ Xp Xn)))) (lambda ((Xp (-> $$unsorted Bool))) (forall ((Xx $$unsorted)) (not (@ Xp Xx)))))) false)) :rule trans :premises (t36 t37))
% 0.22/0.53 (step t39 (cl (= (not (@ tptp.cNAT tptp.cZERO)) false)) :rule trans :premises (t30 t38))
% 0.22/0.53 (step t40 (cl false) :rule resolution :premises (t1 t39 a3))
% 0.22/0.53 (step t41 (cl (not false)) :rule false)
% 0.22/0.53 (step t42 (cl) :rule resolution :premises (t40 t41))
% 0.22/0.53
% 0.22/0.53 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.Pv4i7G7w5O/cvc5---1.0.5_4851.smt2
% 0.22/0.53 % cvc5---1.0.5 exiting
% 0.22/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------