%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL311-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n022.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 17:25:08 EDT 2024

% Result   : Unsatisfiable 8.94s 9.15s
% Output   : Proof 8.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : LCL311-3 : TPTP v8.2.0. Released v2.3.0.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 27 21:42:24 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.94/9.15  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.HdgMAwYxoO/cvc5---1.0.5_5646.smt2
% 8.94/9.15  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.HdgMAwYxoO/cvc5---1.0.5_5646.smt2
% 8.94/9.18  (assume a0 (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))))
% 8.94/9.18  (assume a1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))))
% 8.94/9.18  (assume a2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 8.94/9.18  (assume a3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))))
% 8.94/9.18  (assume a4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 8.94/9.18  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 8.94/9.18  (assume a6 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.18  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 8.94/9.18  (assume a8 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))))
% 8.94/9.18  (assume a9 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))))
% 8.94/9.18  (assume a10 (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))
% 8.94/9.18  (step t1 (cl (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule or_pos)
% 8.94/9.18  (step t2 (cl (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t1))
% 8.94/9.18  (step t3 (cl (not (= (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (or (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) (not (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (or (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv_pos2)
% 8.94/9.18  (step t4 (cl (= (= (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) true) (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule equiv_simplify)
% 8.94/9.18  (step t5 (cl (not (= (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) true)) (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule equiv1 :premises (t4))
% 8.94/9.18  (step t6 (cl (= (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule all_simplify)
% 8.94/9.18  (step t7 (cl (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule refl)
% 8.94/9.18  (step t8 (cl (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule all_simplify)
% 8.94/9.18  (step t9 (cl (= (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule cong :premises (t7 t8))
% 8.94/9.18  (step t10 (cl (= (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) true)) :rule all_simplify)
% 8.94/9.18  (step t11 (cl (= (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) :rule trans :premises (t9 t10))
% 8.94/9.18  (step t12 (cl (= (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) true)) :rule trans :premises (t6 t11))
% 8.94/9.18  (step t13 (cl (= (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule resolution :premises (t5 t12))
% 8.94/9.18  (step t14 (cl (= (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule refl)
% 8.94/9.18  (step t15 (cl (= (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule refl)
% 8.94/9.18  (step t16 (cl (= (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule refl)
% 8.94/9.18  (step t17 (cl (= (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (or (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule cong :premises (t13 t14 t15 t16))
% 8.94/9.18  (step t18 (cl (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_neg)
% 8.94/9.18  (step t19 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t20)
% 8.94/9.18  (assume t20.a0 (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))
% 8.94/9.18  (assume t20.a1 (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))
% 8.94/9.18  (assume t20.a2 (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))
% 8.94/9.18  (step t20.t1 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t20.t2)
% 8.94/9.18  (assume t20.t2.a0 (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))
% 8.94/9.18  (assume t20.t2.a1 (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))
% 8.94/9.18  (assume t20.t2.a2 (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))
% 8.94/9.18  (step t20.t2.t1 (cl (= (= (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) false) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv_simplify)
% 8.94/9.18  (step t20.t2.t2 (cl (not (= (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) false)) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule equiv1 :premises (t20.t2.t1))
% 8.94/9.18  (step t20.t2.t3 (cl (= (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule symm :premises (t20.t2.a2))
% 8.94/9.18  (step t20.t2.t4 (cl (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule symm :premises (t20.t2.a1))
% 8.94/9.18  (step t20.t2.t5 (cl (= (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule trans :premises (t20.t2.t3 t20.t2.t4))
% 8.94/9.18  (step t20.t2.t6 (cl (= (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule cong :premises (t20.t2.t5))
% 8.94/9.18  (step t20.t2.t7 (cl (= (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) false) (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule equiv_simplify)
% 8.94/9.18  (step t20.t2.t8 (cl (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) false) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule equiv2 :premises (t20.t2.t7))
% 8.94/9.18  (step t20.t2.t9 (cl (not (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule not_not)
% 8.94/9.18  (step t20.t2.t10 (cl (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) false) (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t20.t2.t8 t20.t2.t9))
% 8.94/9.18  (step t20.t2.t11 (cl (= (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) false)) :rule resolution :premises (t20.t2.t10 t20.t2.a0))
% 8.94/9.18  (step t20.t2.t12 (cl (= (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) false)) :rule trans :premises (t20.t2.t6 t20.t2.t11))
% 8.94/9.18  (step t20.t2.t13 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t20.t2.t2 t20.t2.t12))
% 8.94/9.18  (step t20.t2 (cl (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule subproof :discharge (t20.t2.a0 t20.t2.a1 t20.t2.a2))
% 8.94/9.18  (step t20.t3 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule and_pos)
% 8.94/9.18  (step t20.t4 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule and_pos)
% 8.94/9.18  (step t20.t5 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule and_pos)
% 8.94/9.18  (step t20.t6 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t20.t2 t20.t3 t20.t4 t20.t5))
% 8.94/9.18  (step t20.t7 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule reordering :premises (t20.t6))
% 8.94/9.18  (step t20.t8 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule contraction :premises (t20.t7))
% 8.94/9.18  (step t20.t9 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t20.t1 t20.t8))
% 8.94/9.18  (step t20.t10 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.18  (step t20.t11 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t20.t9 t20.t10))
% 8.94/9.18  (step t20.t12 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t20.t11))
% 8.94/9.18  (step t20.t13 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies :premises (t20.t12))
% 8.94/9.18  (step t20.t14 (cl (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_neg)
% 8.94/9.18  (step t20.t15 (cl (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t20.t14 t20.a0 t20.a1 t20.a2))
% 8.94/9.18  (step t20.t16 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t20.t13 t20.t15))
% 8.94/9.18  (step t20 (cl (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule subproof :discharge (t20.a0 t20.a1 t20.a2))
% 8.94/9.18  (step t21 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule and_pos)
% 8.94/9.18  (step t22 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule and_pos)
% 8.94/9.18  (step t23 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule and_pos)
% 8.94/9.18  (step t24 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t20 t21 t22 t23))
% 8.94/9.18  (step t25 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule reordering :premises (t24))
% 8.94/9.18  (step t26 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule contraction :premises (t25))
% 8.94/9.18  (step t27 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t19 t26))
% 8.94/9.18  (step t28 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.18  (step t29 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t27 t28))
% 8.94/9.18  (step t30 (cl (=> (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t29))
% 8.94/9.18  (step t31 (cl (not (and (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies :premises (t30))
% 8.94/9.18  (step t32 (cl (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t18 t31))
% 8.94/9.18  (step t33 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule or_neg)
% 8.94/9.18  (step t34 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule or_neg)
% 8.94/9.18  (step t35 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule or_neg)
% 8.94/9.18  (step t36 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule or_neg)
% 8.94/9.18  (step t37 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t32 t33 t34 t35 t36))
% 8.94/9.18  (step t38 (cl (or (not (not (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t37))
% 8.94/9.18  (step t39 (cl (or (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t3 t17 t38))
% 8.94/9.18  (step t40 (cl (tptp.theorem (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule or :premises (t39))
% 8.94/9.18  (step t41 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t42)
% 8.94/9.18  (assume t42.a0 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))))
% 8.94/9.18  (step t42.t1 (cl (or (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule forall_inst :args ((:= P (tptp.implies tptp.p (tptp.not tptp.p))) (:= Q (tptp.not tptp.p))))
% 8.94/9.18  (step t42.t2 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule or :premises (t42.t1))
% 8.94/9.18  (step t42.t3 (cl (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule resolution :premises (t42.t2 t42.a0))
% 8.94/9.18  (step t42 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule subproof :discharge (t42.a0))
% 8.94/9.18  (step t43 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule resolution :premises (t41 t42))
% 8.94/9.18  (step t44 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (not (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule implies_neg2)
% 8.94/9.18  (step t45 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule resolution :premises (t43 t44))
% 8.94/9.18  (step t46 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule contraction :premises (t45))
% 8.94/9.18  (step t47 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule implies :premises (t46))
% 8.94/9.18  (step t48 (cl (= (tptp.equivalent (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule resolution :premises (t47 a9))
% 8.94/9.18  (step t49 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q)))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t50)
% 8.94/9.18  (assume t50.a0 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))))
% 8.94/9.18  (step t50.t1 (cl (or (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q)))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule forall_inst :args ((:= P (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (:= Q (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))
% 8.94/9.18  (step t50.t2 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q)))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule or :premises (t50.t1))
% 8.94/9.18  (step t50.t3 (cl (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule resolution :premises (t50.t2 t50.a0))
% 8.94/9.18  (step t50 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q)))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule subproof :discharge (t50.a0))
% 8.94/9.18  (step t51 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule resolution :premises (t49 t50))
% 8.94/9.18  (step t52 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies_neg2)
% 8.94/9.18  (step t53 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t51 t52))
% 8.94/9.18  (step t54 (cl (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule contraction :premises (t53))
% 8.94/9.18  (step t55 (cl (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q)))))) (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule implies :premises (t54))
% 8.94/9.18  (step t56 (cl (= (tptp.and (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule resolution :premises (t55 a8))
% 8.94/9.18  (step t57 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t40 a10 t48 t56))
% 8.94/9.18  (step t58 (cl (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule and_neg)
% 8.94/9.18  (step t59 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t60)
% 8.94/9.18  (assume t60.a0 (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))
% 8.94/9.18  (assume t60.a1 (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))
% 8.94/9.18  (step t60.t1 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t60.t2)
% 8.94/9.18  (assume t60.t2.a0 (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))
% 8.94/9.18  (assume t60.t2.a1 (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))
% 8.94/9.18  (step t60.t2.t1 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv_simplify)
% 8.94/9.18  (step t60.t2.t2 (cl (not (= (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true)) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule equiv1 :premises (t60.t2.t1))
% 8.94/9.18  (step t60.t2.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule symm :premises (t60.t2.a1))
% 8.94/9.18  (step t60.t2.t4 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule cong :premises (t60.t2.t3))
% 8.94/9.18  (step t60.t2.t5 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv_simplify)
% 8.94/9.18  (step t60.t2.t6 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv2 :premises (t60.t2.t5))
% 8.94/9.18  (step t60.t2.t7 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true)) :rule resolution :premises (t60.t2.t6 t60.t2.a0))
% 8.94/9.18  (step t60.t2.t8 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) true)) :rule trans :premises (t60.t2.t4 t60.t2.t7))
% 8.94/9.18  (step t60.t2.t9 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t60.t2.t2 t60.t2.t8))
% 8.94/9.18  (step t60.t2 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule subproof :discharge (t60.t2.a0 t60.t2.a1))
% 8.94/9.18  (step t60.t3 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_pos)
% 8.94/9.18  (step t60.t4 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_pos)
% 8.94/9.18  (step t60.t5 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule resolution :premises (t60.t2 t60.t3 t60.t4))
% 8.94/9.18  (step t60.t6 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule reordering :premises (t60.t5))
% 8.94/9.18  (step t60.t7 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule contraction :premises (t60.t6))
% 8.94/9.18  (step t60.t8 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t60.t1 t60.t7))
% 8.94/9.18  (step t60.t9 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.18  (step t60.t10 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t60.t8 t60.t9))
% 8.94/9.18  (step t60.t11 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t60.t10))
% 8.94/9.18  (step t60.t12 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies :premises (t60.t11))
% 8.94/9.18  (step t60.t13 (cl (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule and_neg)
% 8.94/9.18  (step t60.t14 (cl (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t60.t13 t60.a1 t60.a0))
% 8.94/9.18  (step t60.t15 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t60.t12 t60.t14))
% 8.94/9.18  (step t60 (cl (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule subproof :discharge (t60.a0 t60.a1))
% 8.94/9.18  (step t61 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_pos)
% 8.94/9.18  (step t62 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule and_pos)
% 8.94/9.18  (step t63 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule resolution :premises (t60 t61 t62))
% 8.94/9.18  (step t64 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule reordering :premises (t63))
% 8.94/9.18  (step t65 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule contraction :premises (t64))
% 8.94/9.18  (step t66 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t59 t65))
% 8.94/9.18  (step t67 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.18  (step t68 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t66 t67))
% 8.94/9.18  (step t69 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t68))
% 8.94/9.18  (step t70 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies :premises (t69))
% 8.94/9.18  (step t71 (cl (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t58 t70))
% 8.94/9.18  (step t72 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule reordering :premises (t71))
% 8.94/9.18  (step t73 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule or_pos)
% 8.94/9.18  (step t74 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule reordering :premises (t73))
% 8.94/9.18  (step t75 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule or_pos)
% 8.94/9.18  (step t76 (cl (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule reordering :premises (t75))
% 8.94/9.18  (step t77 (cl (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule and_neg)
% 8.94/9.18  (step t78 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t79)
% 8.94/9.18  (assume t79.a0 (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))
% 8.94/9.18  (assume t79.a1 (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))
% 8.94/9.18  (step t79.t1 (cl (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t79.t2)
% 8.94/9.18  (assume t79.t2.a0 (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))
% 8.94/9.18  (assume t79.t2.a1 (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))
% 8.94/9.18  (step t79.t2.t1 (cl (= (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) true) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule equiv_simplify)
% 8.94/9.18  (step t79.t2.t2 (cl (not (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) true)) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule equiv1 :premises (t79.t2.t1))
% 8.94/9.18  (step t79.t2.t3 (cl (= (tptp.not tptp.p) (tptp.not tptp.p))) :rule refl)
% 8.94/9.18  (step t79.t2.t4 (cl (= (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.implies tptp.p (tptp.not tptp.p)))) :rule symm :premises (t79.t2.a1))
% 8.94/9.18  (step t79.t2.t5 (cl (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule symm :premises (t79.t2.t4))
% 8.94/9.18  (step t79.t2.t6 (cl (= (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule cong :premises (t79.t2.t3 t79.t2.t5))
% 8.94/9.18  (step t79.t2.t7 (cl (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule cong :premises (t79.t2.t6))
% 8.94/9.18  (step t79.t2.t8 (cl (= (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) true) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule equiv_simplify)
% 8.94/9.18  (step t79.t2.t9 (cl (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) true) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule equiv2 :premises (t79.t2.t8))
% 8.94/9.18  (step t79.t2.t10 (cl (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) true)) :rule resolution :premises (t79.t2.t9 t79.t2.a0))
% 8.94/9.18  (step t79.t2.t11 (cl (= (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) true)) :rule trans :premises (t79.t2.t7 t79.t2.t10))
% 8.94/9.18  (step t79.t2.t12 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t79.t2.t2 t79.t2.t11))
% 8.94/9.18  (step t79.t2 (cl (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule subproof :discharge (t79.t2.a0 t79.t2.a1))
% 8.94/9.18  (step t79.t3 (cl (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule and_pos)
% 8.94/9.18  (step t79.t4 (cl (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.18  (step t79.t5 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule resolution :premises (t79.t2 t79.t3 t79.t4))
% 8.94/9.18  (step t79.t6 (cl (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule reordering :premises (t79.t5))
% 8.94/9.18  (step t79.t7 (cl (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule contraction :premises (t79.t6))
% 8.94/9.18  (step t79.t8 (cl (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t79.t1 t79.t7))
% 8.94/9.18  (step t79.t9 (cl (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule implies_neg2)
% 8.94/9.18  (step t79.t10 (cl (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule resolution :premises (t79.t8 t79.t9))
% 8.94/9.18  (step t79.t11 (cl (=> (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule contraction :premises (t79.t10))
% 8.94/9.18  (step t79.t12 (cl (not (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule implies :premises (t79.t11))
% 8.94/9.18  (step t79.t13 (cl (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule and_neg)
% 8.94/9.18  (step t79.t14 (cl (and (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t79.t13 t79.a1 t79.a0))
% 8.94/9.18  (step t79.t15 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t79.t12 t79.t14))
% 8.94/9.18  (step t79 (cl (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule subproof :discharge (t79.a0 t79.a1))
% 8.94/9.18  (step t80 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.18  (step t81 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule and_pos)
% 8.94/9.18  (step t82 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule resolution :premises (t79 t80 t81))
% 8.94/9.18  (step t83 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule reordering :premises (t82))
% 8.94/9.18  (step t84 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule contraction :premises (t83))
% 8.94/9.18  (step t85 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t78 t84))
% 8.94/9.18  (step t86 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule implies_neg2)
% 8.94/9.18  (step t87 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule resolution :premises (t85 t86))
% 8.94/9.18  (step t88 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) :rule contraction :premises (t87))
% 8.94/9.18  (step t89 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule implies :premises (t88))
% 8.94/9.18  (step t90 (cl (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t77 t89))
% 8.94/9.18  (step t91 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t92)
% 8.94/9.18  (assume t92.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 8.94/9.18  (step t92.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule forall_inst :args ((:= X tptp.p) (:= Y (tptp.not tptp.p))))
% 8.94/9.18  (step t92.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule or :premises (t92.t1))
% 8.94/9.18  (step t92.t3 (cl (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule resolution :premises (t92.t2 t92.a0))
% 8.94/9.18  (step t92 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule subproof :discharge (t92.a0))
% 8.94/9.18  (step t93 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule resolution :premises (t91 t92))
% 8.94/9.18  (step t94 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule implies_neg2)
% 8.94/9.18  (step t95 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t93 t94))
% 8.94/9.18  (step t96 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule contraction :premises (t95))
% 8.94/9.18  (step t97 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule implies :premises (t96))
% 8.94/9.18  (step t98 (cl (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule resolution :premises (t97 a5))
% 8.94/9.18  (step t99 (cl (not (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule or_pos)
% 8.94/9.18  (step t100 (cl (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))))) :rule reordering :premises (t99))
% 8.94/9.18  (step t101 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t102)
% 8.94/9.18  (assume t102.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))))
% 8.94/9.18  (step t102.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule forall_inst :args ((:= A (tptp.not tptp.p)) (:= B (tptp.not tptp.p))))
% 8.94/9.18  (step t102.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule or :premises (t102.t1))
% 8.94/9.18  (step t102.t3 (cl (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t102.t2 t102.a0))
% 8.94/9.18  (step t102 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule subproof :discharge (t102.a0))
% 8.94/9.18  (step t103 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t101 t102))
% 8.94/9.18  (step t104 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule implies_neg2)
% 8.94/9.18  (step t105 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule resolution :premises (t103 t104))
% 8.94/9.18  (step t106 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule contraction :premises (t105))
% 8.94/9.18  (step t107 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule implies :premises (t106))
% 8.94/9.18  (step t108 (cl (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t107 a1))
% 8.94/9.18  (step t109 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t110)
% 8.94/9.18  (assume t110.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.18  (step t110.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))
% 8.94/9.18  (step t110.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule or :premises (t110.t1))
% 8.94/9.18  (step t110.t3 (cl (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule resolution :premises (t110.t2 t110.a0))
% 8.94/9.18  (step t110 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule subproof :discharge (t110.a0))
% 8.94/9.18  (step t111 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule resolution :premises (t109 t110))
% 8.94/9.18  (step t112 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) (not (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t113 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))))) :rule resolution :premises (t111 t112))
% 8.94/9.18  (step t114 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))))) :rule contraction :premises (t113))
% 8.94/9.18  (step t115 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule implies :premises (t114))
% 8.94/9.18  (step t116 (cl (or (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))))) :rule resolution :premises (t115 a6))
% 8.94/9.18  (step t117 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t100 t108 t116))
% 8.94/9.18  (step t118 (cl (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) :rule resolution :premises (t90 t98 t117))
% 8.94/9.18  (step t119 (cl (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule and_neg)
% 8.94/9.18  (step t120 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t121)
% 8.94/9.18  (assume t121.a0 (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (assume t121.a1 (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t121.t1 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t121.t2)
% 8.94/9.18  (assume t121.t2.a0 (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (assume t121.t2.a1 (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t121.t2.t1 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv_simplify)
% 8.94/9.18  (step t121.t2.t2 (cl (not (= (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule equiv1 :premises (t121.t2.t1))
% 8.94/9.18  (step t121.t2.t3 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule symm :premises (t121.t2.a1))
% 8.94/9.18  (step t121.t2.t4 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule cong :premises (t121.t2.t3))
% 8.94/9.18  (step t121.t2.t5 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv_simplify)
% 8.94/9.18  (step t121.t2.t6 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv2 :premises (t121.t2.t5))
% 8.94/9.18  (step t121.t2.t7 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) :rule resolution :premises (t121.t2.t6 t121.t2.a0))
% 8.94/9.18  (step t121.t2.t8 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) :rule trans :premises (t121.t2.t4 t121.t2.t7))
% 8.94/9.18  (step t121.t2.t9 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t121.t2.t2 t121.t2.t8))
% 8.94/9.18  (step t121.t2 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t121.t2.a0 t121.t2.a1))
% 8.94/9.18  (step t121.t3 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t121.t4 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t121.t5 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t121.t2 t121.t3 t121.t4))
% 8.94/9.18  (step t121.t6 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t121.t5))
% 8.94/9.18  (step t121.t7 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t121.t6))
% 8.94/9.18  (step t121.t8 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t121.t1 t121.t7))
% 8.94/9.18  (step t121.t9 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t121.t10 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t121.t8 t121.t9))
% 8.94/9.18  (step t121.t11 (cl (=> (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t121.t10))
% 8.94/9.18  (step t121.t12 (cl (not (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t121.t11))
% 8.94/9.18  (step t121.t13 (cl (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule and_neg)
% 8.94/9.18  (step t121.t14 (cl (and (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t121.t13 t121.a1 t121.a0))
% 8.94/9.18  (step t121.t15 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t121.t12 t121.t14))
% 8.94/9.18  (step t121 (cl (not (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t121.a0 t121.a1))
% 8.94/9.18  (step t122 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t123 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t124 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t121 t122 t123))
% 8.94/9.18  (step t125 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t124))
% 8.94/9.18  (step t126 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t125))
% 8.94/9.18  (step t127 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t120 t126))
% 8.94/9.18  (step t128 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t129 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t127 t128))
% 8.94/9.18  (step t130 (cl (=> (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t129))
% 8.94/9.18  (step t131 (cl (not (and (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t130))
% 8.94/9.18  (step t132 (cl (not (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t119 t131))
% 8.94/9.18  (step t133 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv_pos2)
% 8.94/9.18  (step t134 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))) :rule refl)
% 8.94/9.18  (step t135 (cl (= (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule all_simplify)
% 8.94/9.18  (step t136 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule cong :premises (t134 t135))
% 8.94/9.18  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t138)
% 8.94/9.18  (assume t138.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 8.94/9.18  (step t138.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (:= Y (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t138.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule or :premises (t138.t1))
% 8.94/9.18  (step t138.t3 (cl (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t138.t2 t138.a0))
% 8.94/9.18  (step t138 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t138.a0))
% 8.94/9.18  (step t139 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t137 t138))
% 8.94/9.18  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t139 t140))
% 8.94/9.18  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t141))
% 8.94/9.18  (step t143 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t133 t136 t142))
% 8.94/9.18  (step t144 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t143))
% 8.94/9.18  (step t145 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t144 a5))
% 8.94/9.18  (step t146 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule or_pos)
% 8.94/9.18  (step t147 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule reordering :premises (t146))
% 8.94/9.18  (step t148 (cl (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule and_neg)
% 8.94/9.18  (step t149 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t150)
% 8.94/9.18  (assume t150.a0 (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (assume t150.a1 (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t150.t1 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t150.t2)
% 8.94/9.18  (assume t150.t2.a0 (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (assume t150.t2.a1 (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t150.t2.t1 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv_simplify)
% 8.94/9.18  (step t150.t2.t2 (cl (not (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule equiv1 :premises (t150.t2.t1))
% 8.94/9.18  (step t150.t2.t3 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule symm :premises (t150.t2.a1))
% 8.94/9.18  (step t150.t2.t4 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule cong :premises (t150.t2.t3))
% 8.94/9.18  (step t150.t2.t5 (cl (= (= (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv_simplify)
% 8.94/9.18  (step t150.t2.t6 (cl (= (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule equiv2 :premises (t150.t2.t5))
% 8.94/9.18  (step t150.t2.t7 (cl (= (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) :rule resolution :premises (t150.t2.t6 t150.t2.a0))
% 8.94/9.18  (step t150.t2.t8 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) true)) :rule trans :premises (t150.t2.t4 t150.t2.t7))
% 8.94/9.18  (step t150.t2.t9 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t150.t2.t2 t150.t2.t8))
% 8.94/9.18  (step t150.t2 (cl (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t150.t2.a0 t150.t2.a1))
% 8.94/9.18  (step t150.t3 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t150.t4 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t150.t5 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t150.t2 t150.t3 t150.t4))
% 8.94/9.18  (step t150.t6 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t150.t5))
% 8.94/9.18  (step t150.t7 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t150.t6))
% 8.94/9.18  (step t150.t8 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t150.t1 t150.t7))
% 8.94/9.18  (step t150.t9 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t150.t10 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t150.t8 t150.t9))
% 8.94/9.18  (step t150.t11 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t150.t10))
% 8.94/9.18  (step t150.t12 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t150.t11))
% 8.94/9.18  (step t150.t13 (cl (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule and_neg)
% 8.94/9.18  (step t150.t14 (cl (and (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t150.t13 t150.a1 t150.a0))
% 8.94/9.18  (step t150.t15 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t150.t12 t150.t14))
% 8.94/9.18  (step t150 (cl (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t150.a0 t150.a1))
% 8.94/9.18  (step t151 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t152 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule and_pos)
% 8.94/9.18  (step t153 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t150 t151 t152))
% 8.94/9.18  (step t154 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t153))
% 8.94/9.18  (step t155 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t154))
% 8.94/9.18  (step t156 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t149 t155))
% 8.94/9.18  (step t157 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t158 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t156 t157))
% 8.94/9.18  (step t159 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t158))
% 8.94/9.18  (step t160 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t159))
% 8.94/9.18  (step t161 (cl (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t148 t160))
% 8.94/9.18  (step t162 (cl (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t161))
% 8.94/9.18  (step t163 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule or_pos)
% 8.94/9.18  (step t164 (cl (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule reordering :premises (t163))
% 8.94/9.18  (step t165 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t166)
% 8.94/9.18  (assume t166.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 8.94/9.18  (step t166.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (:= B (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))
% 8.94/9.18  (step t166.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule or :premises (t166.t1))
% 8.94/9.18  (step t166.t3 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t166.t2 t166.a0))
% 8.94/9.18  (step t166 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t166.a0))
% 8.94/9.18  (step t167 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t165 t166))
% 8.94/9.18  (step t168 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t169 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t167 t168))
% 8.94/9.18  (step t170 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t169))
% 8.94/9.18  (step t171 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t170))
% 8.94/9.18  (step t172 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t171 a2))
% 8.94/9.18  (step t173 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t174)
% 8.94/9.18  (assume t174.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.18  (step t174.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))
% 8.94/9.18  (step t174.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule or :premises (t174.t1))
% 8.94/9.18  (step t174.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t174.t2 t174.a0))
% 8.94/9.18  (step t174 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule subproof :discharge (t174.a0))
% 8.94/9.18  (step t175 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t173 t174))
% 8.94/9.18  (step t176 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.18  (step t177 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule resolution :premises (t175 t176))
% 8.94/9.18  (step t178 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule contraction :premises (t177))
% 8.94/9.18  (step t179 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule implies :premises (t178))
% 8.94/9.18  (step t180 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t179 a6))
% 8.94/9.18  (step t181 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t164 t172 t180))
% 8.94/9.18  (step t182 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t183)
% 8.94/9.18  (assume t183.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 8.94/9.18  (step t183.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (:= Y (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.18  (step t183.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule or :premises (t183.t1))
% 8.94/9.18  (step t183.t3 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t183.t2 t183.a0))
% 8.94/9.18  (step t183 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule subproof :discharge (t183.a0))
% 8.94/9.18  (step t184 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t182 t183))
% 8.94/9.18  (step t185 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.18  (step t186 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t184 t185))
% 8.94/9.18  (step t187 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule contraction :premises (t186))
% 8.94/9.18  (step t188 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies :premises (t187))
% 8.94/9.18  (step t189 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t188 a5))
% 8.94/9.18  (step t190 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t162 t181 t189))
% 8.94/9.18  (step t191 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule or_pos)
% 8.94/9.18  (step t192 (cl (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))))) :rule reordering :premises (t191))
% 8.94/9.18  (step t193 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t194)
% 8.94/9.18  (assume t194.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))))
% 8.94/9.18  (step t194.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (:= B (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))) (:= C (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))
% 8.94/9.18  (step t194.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule or :premises (t194.t1))
% 8.94/9.18  (step t194.t3 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t194.t2 t194.a0))
% 8.94/9.18  (step t194 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule subproof :discharge (t194.a0))
% 8.94/9.18  (step t195 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t193 t194))
% 8.94/9.18  (step t196 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule implies_neg2)
% 8.94/9.18  (step t197 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t195 t196))
% 8.94/9.18  (step t198 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule contraction :premises (t197))
% 8.94/9.18  (step t199 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies :premises (t198))
% 8.94/9.18  (step t200 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t199 a3))
% 8.94/9.18  (step t201 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 8.94/9.18  (anchor :step t202)
% 8.94/9.18  (assume t202.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.18  (step t202.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))
% 8.94/9.18  (step t202.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule or :premises (t202.t1))
% 8.94/9.18  (step t202.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule resolution :premises (t202.t2 t202.a0))
% 8.94/9.18  (step t202 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule subproof :discharge (t202.a0))
% 8.94/9.18  (step t203 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule resolution :premises (t201 t202))
% 8.94/9.18  (step t204 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))))) :rule implies_neg2)
% 8.94/9.18  (step t205 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))))) :rule resolution :premises (t203 t204))
% 8.94/9.19  (step t206 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))))) :rule contraction :premises (t205))
% 8.94/9.19  (step t207 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule implies :premises (t206))
% 8.94/9.19  (step t208 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule resolution :premises (t207 a6))
% 8.94/9.19  (step t209 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t192 t200 t208))
% 8.94/9.19  (step t210 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t211)
% 8.94/9.19  (assume t211.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 8.94/9.19  (step t211.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (:= Y (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))
% 8.94/9.19  (step t211.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule or :premises (t211.t1))
% 8.94/9.19  (step t211.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t211.t2 t211.a0))
% 8.94/9.19  (step t211 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule subproof :discharge (t211.a0))
% 8.94/9.19  (step t212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t210 t211))
% 8.94/9.19  (step t213 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.19  (step t214 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule resolution :premises (t212 t213))
% 8.94/9.19  (step t215 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))))) :rule contraction :premises (t214))
% 8.94/9.19  (step t216 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule implies :premises (t215))
% 8.94/9.19  (step t217 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t216 a7))
% 8.94/9.19  (step t218 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t147 t190 t209 t217))
% 8.94/9.19  (step t219 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t132 t145 t218))
% 8.94/9.19  (step t220 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t221)
% 8.94/9.19  (assume t221.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 8.94/9.19  (step t221.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (:= Y (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))
% 8.94/9.19  (step t221.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule or :premises (t221.t1))
% 8.94/9.19  (step t221.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule resolution :premises (t221.t2 t221.a0))
% 8.94/9.19  (step t221 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule subproof :discharge (t221.a0))
% 8.94/9.19  (step t222 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule resolution :premises (t220 t221))
% 8.94/9.19  (step t223 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule implies_neg2)
% 8.94/9.19  (step t224 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule resolution :premises (t222 t223))
% 8.94/9.19  (step t225 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) :rule contraction :premises (t224))
% 8.94/9.19  (step t226 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule implies :premises (t225))
% 8.94/9.19  (step t227 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) :rule resolution :premises (t226 a7))
% 8.94/9.19  (step t228 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t76 t118 t219 t227))
% 8.94/9.19  (step t229 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule or_pos)
% 8.94/9.19  (step t230 (cl (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))))) :rule reordering :premises (t229))
% 8.94/9.19  (step t231 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t232)
% 8.94/9.19  (assume t232.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 8.94/9.19  (step t232.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (:= B (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))
% 8.94/9.19  (step t232.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule or :premises (t232.t1))
% 8.94/9.19  (step t232.t3 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t232.t2 t232.a0))
% 8.94/9.19  (step t232 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule subproof :discharge (t232.a0))
% 8.94/9.19  (step t233 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t231 t232))
% 8.94/9.19  (step t234 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule implies_neg2)
% 8.94/9.19  (step t235 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule resolution :premises (t233 t234))
% 8.94/9.19  (step t236 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule contraction :premises (t235))
% 8.94/9.19  (step t237 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies :premises (t236))
% 8.94/9.19  (step t238 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t237 a2))
% 8.94/9.19  (step t239 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t240)
% 8.94/9.19  (assume t240.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.19  (step t240.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))
% 8.94/9.19  (step t240.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule or :premises (t240.t1))
% 8.94/9.19  (step t240.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule resolution :premises (t240.t2 t240.a0))
% 8.94/9.19  (step t240 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule subproof :discharge (t240.a0))
% 8.94/9.19  (step t241 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule resolution :premises (t239 t240))
% 8.94/9.19  (step t242 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))))) :rule implies_neg2)
% 8.94/9.19  (step t243 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))))) :rule resolution :premises (t241 t242))
% 8.94/9.19  (step t244 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))))) :rule contraction :premises (t243))
% 8.94/9.19  (step t245 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule implies :premises (t244))
% 8.94/9.19  (step t246 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))))) :rule resolution :premises (t245 a6))
% 8.94/9.19  (step t247 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t230 t238 t246))
% 8.94/9.19  (step t248 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t249)
% 8.94/9.19  (assume t249.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 8.94/9.19  (step t249.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (:= Y (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))
% 8.94/9.19  (step t249.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule or :premises (t249.t1))
% 8.94/9.19  (step t249.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t249.t2 t249.a0))
% 8.94/9.19  (step t249 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule subproof :discharge (t249.a0))
% 8.94/9.19  (step t250 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t248 t249))
% 8.94/9.19  (step t251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule implies_neg2)
% 8.94/9.19  (step t252 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule resolution :premises (t250 t251))
% 8.94/9.19  (step t253 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))))) :rule contraction :premises (t252))
% 8.94/9.19  (step t254 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule implies :premises (t253))
% 8.94/9.19  (step t255 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))) (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))))) :rule resolution :premises (t254 a7))
% 8.94/9.19  (step t256 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t74 t228 t247 t255))
% 8.94/9.19  (step t257 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule equiv_pos2)
% 8.94/9.19  (step t258 (cl (= (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule all_simplify)
% 8.94/9.19  (step t259 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))))) :rule cong :premises (t134 t258))
% 8.94/9.19  (step t260 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t261)
% 8.94/9.19  (assume t261.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 8.94/9.19  (step t261.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (:= Y (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))
% 8.94/9.19  (step t261.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule or :premises (t261.t1))
% 8.94/9.19  (step t261.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t261.t2 t261.a0))
% 8.94/9.19  (step t261 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule subproof :discharge (t261.a0))
% 8.94/9.19  (step t262 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t260 t261))
% 8.94/9.19  (step t263 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule implies_neg2)
% 8.94/9.19  (step t264 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t262 t263))
% 8.94/9.19  (step t265 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule contraction :premises (t264))
% 8.94/9.19  (step t266 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p)))))))))) :rule resolution :premises (t257 t259 t265))
% 8.94/9.19  (step t267 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule implies :premises (t266))
% 8.94/9.19  (step t268 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t267 a5))
% 8.94/9.19  (step t269 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) :rule resolution :premises (t72 t256 t268))
% 8.94/9.19  (step t270 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t271)
% 8.94/9.19  (assume t271.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 8.94/9.19  (step t271.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (:= Y (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))
% 8.94/9.19  (step t271.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule or :premises (t271.t1))
% 8.94/9.19  (step t271.t3 (cl (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t271.t2 t271.a0))
% 8.94/9.19  (step t271 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule subproof :discharge (t271.a0))
% 8.94/9.19  (step t272 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t270 t271))
% 8.94/9.19  (step t273 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies_neg2)
% 8.94/9.19  (step t274 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t272 t273))
% 8.94/9.19  (step t275 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t274))
% 8.94/9.19  (step t276 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule implies :premises (t275))
% 8.94/9.19  (step t277 (cl (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.not (tptp.or (tptp.not (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.not (tptp.implies (tptp.not tptp.p) (tptp.implies tptp.p (tptp.not tptp.p))))))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t276 a7))
% 8.94/9.19  (step t278 (cl (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule and_neg)
% 8.94/9.19  (step t279 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t280)
% 8.94/9.19  (assume t280.a0 (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))
% 8.94/9.19  (assume t280.a1 (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))
% 8.94/9.19  (step t280.t1 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t280.t2)
% 8.94/9.19  (assume t280.t2.a0 (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))
% 8.94/9.19  (assume t280.t2.a1 (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))
% 8.94/9.19  (step t280.t2.t1 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) true) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule equiv_simplify)
% 8.94/9.19  (step t280.t2.t2 (cl (not (= (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) true)) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule equiv1 :premises (t280.t2.t1))
% 8.94/9.19  (step t280.t2.t3 (cl (= (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.implies tptp.p (tptp.not tptp.p)))) :rule symm :premises (t280.t2.a1))
% 8.94/9.19  (step t280.t2.t4 (cl (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule symm :premises (t280.t2.t3))
% 8.94/9.19  (step t280.t2.t5 (cl (= (tptp.not tptp.p) (tptp.not tptp.p))) :rule refl)
% 8.94/9.19  (step t280.t2.t6 (cl (= (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)) (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule cong :premises (t280.t2.t4 t280.t2.t5))
% 8.94/9.19  (step t280.t2.t7 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule cong :premises (t280.t2.t6))
% 8.94/9.19  (step t280.t2.t8 (cl (= (= (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) true) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule equiv_simplify)
% 8.94/9.19  (step t280.t2.t9 (cl (= (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) true) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule equiv2 :premises (t280.t2.t8))
% 8.94/9.19  (step t280.t2.t10 (cl (= (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) true)) :rule resolution :premises (t280.t2.t9 t280.t2.a0))
% 8.94/9.19  (step t280.t2.t11 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) true)) :rule trans :premises (t280.t2.t7 t280.t2.t10))
% 8.94/9.19  (step t280.t2.t12 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t280.t2.t2 t280.t2.t11))
% 8.94/9.19  (step t280.t2 (cl (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule subproof :discharge (t280.t2.a0 t280.t2.a1))
% 8.94/9.19  (step t280.t3 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.19  (step t280.t4 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.19  (step t280.t5 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))))) :rule resolution :premises (t280.t2 t280.t3 t280.t4))
% 8.94/9.19  (step t280.t6 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule reordering :premises (t280.t5))
% 8.94/9.19  (step t280.t7 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule contraction :premises (t280.t6))
% 8.94/9.19  (step t280.t8 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t280.t1 t280.t7))
% 8.94/9.19  (step t280.t9 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule implies_neg2)
% 8.94/9.19  (step t280.t10 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule resolution :premises (t280.t8 t280.t9))
% 8.94/9.19  (step t280.t11 (cl (=> (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule contraction :premises (t280.t10))
% 8.94/9.19  (step t280.t12 (cl (not (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule implies :premises (t280.t11))
% 8.94/9.19  (step t280.t13 (cl (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule and_neg)
% 8.94/9.19  (step t280.t14 (cl (and (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))))) :rule resolution :premises (t280.t13 t280.a1 t280.a0))
% 8.94/9.19  (step t280.t15 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t280.t12 t280.t14))
% 8.94/9.19  (step t280 (cl (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule subproof :discharge (t280.a0 t280.a1))
% 8.94/9.19  (step t281 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.19  (step t282 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule and_pos)
% 8.94/9.19  (step t283 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t280 t281 t282))
% 8.94/9.19  (step t284 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule reordering :premises (t283))
% 8.94/9.19  (step t285 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule contraction :premises (t284))
% 8.94/9.19  (step t286 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t279 t285))
% 8.94/9.19  (step t287 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule implies_neg2)
% 8.94/9.19  (step t288 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule resolution :premises (t286 t287))
% 8.94/9.19  (step t289 (cl (=> (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule contraction :premises (t288))
% 8.94/9.19  (step t290 (cl (not (and (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule implies :premises (t289))
% 8.94/9.19  (step t291 (cl (not (= (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t278 t290))
% 8.94/9.19  (step t292 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule or_pos)
% 8.94/9.19  (step t293 (cl (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule reordering :premises (t292))
% 8.94/9.19  (step t294 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t295)
% 8.94/9.19  (assume t295.a0 (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))))
% 8.94/9.19  (step t295.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule forall_inst :args ((:= A (tptp.not tptp.p))))
% 8.94/9.19  (step t295.t2 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule or :premises (t295.t1))
% 8.94/9.19  (step t295.t3 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t295.t2 t295.a0))
% 8.94/9.19  (step t295 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule subproof :discharge (t295.a0))
% 8.94/9.19  (step t296 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t294 t295))
% 8.94/9.19  (step t297 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule implies_neg2)
% 8.94/9.19  (step t298 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule resolution :premises (t296 t297))
% 8.94/9.19  (step t299 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))) :rule contraction :premises (t298))
% 8.94/9.19  (step t300 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule implies :premises (t299))
% 8.94/9.19  (step t301 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t300 a0))
% 8.94/9.19  (step t302 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 8.94/9.19  (anchor :step t303)
% 8.94/9.19  (assume t303.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 8.94/9.19  (step t303.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))
% 8.94/9.19  (step t303.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule or :premises (t303.t1))
% 8.94/9.19  (step t303.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t303.t2 t303.a0))
% 8.94/9.19  (step t303 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule subproof :discharge (t303.a0))
% 8.94/9.19  (step t304 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t302 t303))
% 8.94/9.19  (step t305 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule implies_neg2)
% 8.94/9.19  (step t306 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule resolution :premises (t304 t305))
% 8.94/9.19  (step t307 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))))))) :rule contraction :premises (t306))
% 8.94/9.19  (step t308 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule implies :premises (t307))
% 8.94/9.19  (step t309 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))))) :rule resolution :premises (t308 a6))
% 8.94/9.19  (step t310 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not tptp.p) (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t293 t301 t309))
% 8.94/9.19  (step t311 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.p (tptp.not tptp.p)) (tptp.not tptp.p)))) :rule resolution :premises (t291 t98 t310))
% 8.94/9.19  (step t312 (cl) :rule resolution :premises (t2 t57 t269 t277 t311))
% 8.94/9.19  
% 8.94/9.21  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.HdgMAwYxoO/cvc5---1.0.5_5646.smt2
% 9.05/9.21  % cvc5---1.0.5 exiting
% 9.05/9.22  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------