TSTP Solution File: LCL194-3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL194-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n013.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 17:24:50 EDT 2024
% Result : Unsatisfiable 28.68s 28.84s
% Output : Proof 28.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL194-3 : TPTP v8.2.0. Released v2.3.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 21:23:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.50/10.70 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.57/15.76 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.61/20.81 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.64/25.86 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.68/28.84 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.NiWy94TbTR/cvc5---1.0.5_3503.smt2
% 28.68/28.84 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.NiWy94TbTR/cvc5---1.0.5_3503.smt2
% 28.68/28.86 (assume a0 (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))))
% 28.68/28.86 (assume a1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))))
% 28.68/28.86 (assume a2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 28.68/28.86 (assume a3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))))
% 28.68/28.86 (assume a4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 28.68/28.86 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.86 (assume a6 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.86 (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 28.68/28.86 (assume a8 (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))
% 28.68/28.86 (step t1 (cl (not (= (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv_pos2)
% 28.68/28.86 (step t2 (cl (= (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule refl)
% 28.68/28.86 (step t3 (cl (= (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))))) :rule refl)
% 28.68/28.86 (step t4 (cl (= (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule refl)
% 28.68/28.86 (step t5 (cl (= (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule refl)
% 28.68/28.86 (step t6 (cl (= (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule refl)
% 28.68/28.86 (step t7 (cl (= (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) true) (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule equiv_simplify)
% 28.68/28.86 (step t8 (cl (not (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) true)) (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv1 :premises (t7))
% 28.68/28.86 (step t9 (cl (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule all_simplify)
% 28.68/28.86 (step t10 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule refl)
% 28.68/28.86 (step t11 (cl (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule all_simplify)
% 28.68/28.86 (step t12 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule cong :premises (t10 t11))
% 28.68/28.86 (step t13 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) true)) :rule all_simplify)
% 28.68/28.86 (step t14 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) true)) :rule trans :premises (t12 t13))
% 28.68/28.86 (step t15 (cl (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) true)) :rule trans :premises (t9 t14))
% 28.68/28.86 (step t16 (cl (= (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t8 t15))
% 28.68/28.86 (step t17 (cl (= (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule cong :premises (t2 t3 t4 t5 t6 t16))
% 28.68/28.86 (step t18 (cl (not (= (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) (not (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule equiv_pos2)
% 28.68/28.86 (step t19 (cl (= (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule refl)
% 28.68/28.86 (step t20 (cl (= (= (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule equiv_simplify)
% 28.68/28.86 (step t21 (cl (= (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (not (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule equiv2 :premises (t20))
% 28.68/28.86 (step t22 (cl (not (not (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule not_not)
% 28.68/28.86 (step t23 (cl (= (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t21 t22))
% 28.68/28.86 (step t24 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg1)
% 28.68/28.86 (anchor :step t25)
% 28.68/28.86 (assume t25.a0 (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))
% 28.68/28.86 (assume t25.a1 (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))
% 28.68/28.86 (assume t25.a2 (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.86 (assume t25.a3 (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))
% 28.68/28.86 (assume t25.a4 (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.86 (assume t25.a5 (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.86 (step t25.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 28.68/28.86 (step t25.t2 (cl (= (= true false) false)) :rule all_simplify)
% 28.68/28.86 (step t25.t3 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.86 (step t25.t4 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv2 :premises (t25.t3))
% 28.68/28.86 (step t25.t5 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true)) :rule resolution :premises (t25.t4 t25.a5))
% 28.68/28.86 (step t25.t6 (cl (= true (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule symm :premises (t25.t5))
% 28.68/28.86 (step t25.t7 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule symm :premises (t25.a4))
% 28.68/28.86 (step t25.t8 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule symm :premises (t25.t7))
% 28.68/28.86 (step t25.t9 (cl (= (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule symm :premises (t25.a1))
% 28.68/28.86 (step t25.t10 (cl (= (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule refl)
% 28.68/28.86 (step t25.t11 (cl (= (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) :rule symm :premises (t25.a3))
% 28.68/28.86 (step t25.t12 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule cong :premises (t25.t10 t25.t11))
% 28.68/28.86 (step t25.t13 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule symm :premises (t25.a2))
% 28.68/28.86 (step t25.t14 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule trans :premises (t25.t12 t25.t13))
% 28.68/28.86 (step t25.t15 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule cong :premises (t25.t9 t25.t14))
% 28.68/28.86 (step t25.t16 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule trans :premises (t25.t8 t25.t15))
% 28.68/28.86 (step t25.t17 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule cong :premises (t25.t16))
% 28.68/28.86 (step t25.t18 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) false) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule equiv_simplify)
% 28.68/28.86 (step t25.t19 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) false) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule equiv2 :premises (t25.t18))
% 28.68/28.86 (step t25.t20 (cl (not (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule not_not)
% 28.68/28.86 (step t25.t21 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) false) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t25.t19 t25.t20))
% 28.68/28.86 (step t25.t22 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) false)) :rule resolution :premises (t25.t21 t25.a0))
% 28.68/28.86 (step t25.t23 (cl (= true false)) :rule trans :premises (t25.t6 t25.t17 t25.t22))
% 28.68/28.86 (step t25.t24 (cl false) :rule resolution :premises (t25.t1 t25.t2 t25.t23))
% 28.68/28.86 (step t25 (cl (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) :rule subproof :discharge (t25.a0 t25.a1 t25.a2 t25.a3 t25.a4 t25.a5))
% 28.68/28.86 (step t26 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule and_pos)
% 28.68/28.86 (step t27 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule and_pos)
% 28.68/28.86 (step t28 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.86 (step t29 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule and_pos)
% 28.68/28.86 (step t30 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.86 (step t31 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.86 (step t32 (cl false (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t25 t26 t27 t28 t29 t30 t31))
% 28.68/28.86 (step t33 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) false) :rule reordering :premises (t32))
% 28.68/28.86 (step t34 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) false) :rule contraction :premises (t33))
% 28.68/28.86 (step t35 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) false) :rule resolution :premises (t24 t34))
% 28.68/28.86 (step t36 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (not false)) :rule implies_neg2)
% 28.68/28.86 (step t37 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false)) :rule resolution :premises (t35 t36))
% 28.68/28.86 (step t38 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false)) :rule contraction :premises (t37))
% 28.68/28.86 (step t39 (cl (= (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule implies_simplify)
% 28.68/28.86 (step t40 (cl (not (=> (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false)) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule equiv1 :premises (t39))
% 28.68/28.86 (step t41 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t38 t40))
% 28.68/28.86 (step t42 (cl (= (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) false)) :rule resolution :premises (t23 t41))
% 28.68/28.86 (step t43 (cl (= (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) false))) :rule cong :premises (t19 t42))
% 28.68/28.86 (step t44 (cl (= (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) false) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule all_simplify)
% 28.68/28.86 (step t45 (cl (= (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule trans :premises (t43 t44))
% 28.68/28.86 (step t46 (cl (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg1)
% 28.68/28.86 (anchor :step t47)
% 28.68/28.86 (assume t47.a0 (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))
% 28.68/28.86 (assume t47.a1 (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))
% 28.68/28.86 (assume t47.a2 (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.86 (assume t47.a3 (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.86 (assume t47.a4 (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.86 (assume t47.a5 (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))
% 28.68/28.86 (step t47.t1 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule and_neg)
% 28.68/28.86 (step t47.t2 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t47.t1 t47.a5 t47.a1 t47.a2 t47.a0 t47.a3 t47.a4))
% 28.68/28.86 (step t47 (cl (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t47.a0 t47.a1 t47.a2 t47.a3 t47.a4 t47.a5))
% 28.68/28.86 (step t48 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule and_pos)
% 28.68/28.86 (step t49 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule and_pos)
% 28.68/28.86 (step t50 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.86 (step t51 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.86 (step t52 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.86 (step t53 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule and_pos)
% 28.68/28.86 (step t54 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t47 t48 t49 t50 t51 t52 t53))
% 28.68/28.86 (step t55 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule reordering :premises (t54))
% 28.68/28.86 (step t56 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t55))
% 28.68/28.86 (step t57 (cl (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t46 t56))
% 28.68/28.86 (step t58 (cl (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.86 (step t59 (cl (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t57 t58))
% 28.68/28.86 (step t60 (cl (=> (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (and (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t59))
% 28.68/28.86 (step t61 (cl (not (and (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t18 t45 t60))
% 28.68/28.86 (step t62 (cl (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule not_and :premises (t61))
% 28.68/28.86 (step t63 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule or_neg)
% 28.68/28.86 (step t64 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))))) :rule or_neg)
% 28.68/28.86 (step t65 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule or_neg)
% 28.68/28.86 (step t66 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule or_neg)
% 28.68/28.86 (step t67 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule or_neg)
% 28.68/28.86 (step t68 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule or_neg)
% 28.68/28.86 (step t69 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t62 t63 t64 t65 t66 t67 t68))
% 28.68/28.86 (step t70 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule contraction :premises (t69))
% 28.68/28.86 (step t71 (cl (or (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t1 t17 t70))
% 28.68/28.86 (step t72 (cl (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule or :premises (t71))
% 28.68/28.87 (step t73 (cl (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule or_pos)
% 28.68/28.87 (step t74 (cl (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule reordering :premises (t73))
% 28.68/28.87 (step t75 (cl (not (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule or_pos)
% 28.68/28.87 (step t76 (cl (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule reordering :premises (t75))
% 28.68/28.87 (step t77 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t78)
% 28.68/28.87 (assume t78.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 28.68/28.87 (step t78.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.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule forall_inst :args ((:= A tptp.q) (:= B tptp.p)))
% 28.68/28.87 (step t78.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.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule or :premises (t78.t1))
% 28.68/28.87 (step t78.t3 (cl (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t78.t2 t78.a0))
% 28.68/28.87 (step t78 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule subproof :discharge (t78.a0))
% 28.68/28.87 (step t79 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t77 t78))
% 28.68/28.87 (step t80 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule implies_neg2)
% 28.68/28.87 (step t81 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule resolution :premises (t79 t80))
% 28.68/28.87 (step t82 (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.q tptp.p) (tptp.or tptp.p tptp.q))))) :rule contraction :premises (t81))
% 28.68/28.87 (step t83 (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.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule implies :premises (t82))
% 28.68/28.87 (step t84 (cl (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t83 a2))
% 28.68/28.87 (step t85 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t86)
% 28.68/28.87 (assume t86.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.87 (step t86.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))
% 28.68/28.87 (step t86.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule or :premises (t86.t1))
% 28.68/28.87 (step t86.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t86.t2 t86.a0))
% 28.68/28.87 (step t86 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule subproof :discharge (t86.a0))
% 28.68/28.87 (step t87 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t85 t86))
% 28.68/28.87 (step t88 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (not (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule implies_neg2)
% 28.68/28.87 (step t89 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule resolution :premises (t87 t88))
% 28.68/28.87 (step t90 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule contraction :premises (t89))
% 28.68/28.87 (step t91 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule implies :premises (t90))
% 28.68/28.87 (step t92 (cl (or (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))) (not (tptp.axiom (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t91 a6))
% 28.68/28.87 (step t93 (cl (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t76 t84 t92))
% 28.68/28.87 (step t94 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule or_pos)
% 28.68/28.87 (step t95 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule reordering :premises (t94))
% 28.68/28.87 (step t96 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule or_pos)
% 28.68/28.87 (step t97 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule reordering :premises (t96))
% 28.68/28.87 (step t98 (cl (not (= (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) (not (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv_pos2)
% 28.68/28.87 (step t99 (cl (= (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) true) (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.87 (step t100 (cl (not (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) true)) (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule equiv1 :premises (t99))
% 28.68/28.87 (step t101 (cl (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule all_simplify)
% 28.68/28.87 (step t102 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule refl)
% 28.68/28.87 (step t103 (cl (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule all_simplify)
% 28.68/28.87 (step t104 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule cong :premises (t102 t103))
% 28.68/28.87 (step t105 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) true)) :rule all_simplify)
% 28.68/28.87 (step t106 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) true)) :rule trans :premises (t104 t105))
% 28.68/28.87 (step t107 (cl (= (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) true)) :rule trans :premises (t101 t106))
% 28.68/28.87 (step t108 (cl (= (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t100 t107))
% 28.68/28.87 (step t109 (cl (= (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule refl)
% 28.68/28.87 (step t110 (cl (= (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule refl)
% 28.68/28.87 (step t111 (cl (= (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule cong :premises (t108 t109 t110))
% 28.68/28.87 (step t112 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule and_neg)
% 28.68/28.87 (step t113 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t114)
% 28.68/28.87 (assume t114.a0 (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (assume t114.a1 (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t114.t1 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t114.t2)
% 28.68/28.87 (assume t114.t2.a0 (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (assume t114.t2.a1 (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t114.t2.t1 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.87 (step t114.t2.t2 (cl (not (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false)) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule equiv1 :premises (t114.t2.t1))
% 28.68/28.87 (step t114.t2.t3 (cl (= (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule symm :premises (t114.t2.a1))
% 28.68/28.87 (step t114.t2.t4 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule cong :premises (t114.t2.t3))
% 28.68/28.87 (step t114.t2.t5 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.87 (step t114.t2.t6 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule equiv2 :premises (t114.t2.t5))
% 28.68/28.87 (step t114.t2.t7 (cl (not (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule not_not)
% 28.68/28.87 (step t114.t2.t8 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t114.t2.t6 t114.t2.t7))
% 28.68/28.87 (step t114.t2.t9 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false)) :rule resolution :premises (t114.t2.t8 t114.t2.a0))
% 28.68/28.87 (step t114.t2.t10 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) false)) :rule trans :premises (t114.t2.t4 t114.t2.t9))
% 28.68/28.87 (step t114.t2.t11 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t114.t2.t2 t114.t2.t10))
% 28.68/28.87 (step t114.t2 (cl (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t114.t2.a0 t114.t2.a1))
% 28.68/28.87 (step t114.t3 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t114.t4 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t114.t5 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t114.t2 t114.t3 t114.t4))
% 28.68/28.87 (step t114.t6 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule reordering :premises (t114.t5))
% 28.68/28.87 (step t114.t7 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t114.t6))
% 28.68/28.87 (step t114.t8 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t114.t1 t114.t7))
% 28.68/28.87 (step t114.t9 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t114.t10 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t114.t8 t114.t9))
% 28.68/28.87 (step t114.t11 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t114.t10))
% 28.68/28.87 (step t114.t12 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t114.t11))
% 28.68/28.87 (step t114.t13 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule and_neg)
% 28.68/28.87 (step t114.t14 (cl (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t114.t13 t114.a0 t114.a1))
% 28.68/28.87 (step t114.t15 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t114.t12 t114.t14))
% 28.68/28.87 (step t114 (cl (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t114.a0 t114.a1))
% 28.68/28.87 (step t115 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t116 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t117 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t114 t115 t116))
% 28.68/28.87 (step t118 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule reordering :premises (t117))
% 28.68/28.87 (step t119 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t118))
% 28.68/28.87 (step t120 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t113 t119))
% 28.68/28.87 (step t121 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t122 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t120 t121))
% 28.68/28.87 (step t123 (cl (=> (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t122))
% 28.68/28.87 (step t124 (cl (not (and (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t123))
% 28.68/28.87 (step t125 (cl (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t112 t124))
% 28.68/28.87 (step t126 (cl (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule or_neg)
% 28.68/28.87 (step t127 (cl (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule or_neg)
% 28.68/28.87 (step t128 (cl (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule or_neg)
% 28.68/28.87 (step t129 (cl (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t125 t126 t127 t128))
% 28.68/28.87 (step t130 (cl (or (not (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t129))
% 28.68/28.87 (step t131 (cl (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t98 t111 t130))
% 28.68/28.87 (step t132 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule or :premises (t131))
% 28.68/28.87 (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t134)
% 28.68/28.87 (assume t134.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t134.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.q tptp.r)) (:= Y (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t134.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule or :premises (t134.t1))
% 28.68/28.87 (step t134.t3 (cl (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t134.t2 t134.a0))
% 28.68/28.87 (step t134 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t134.a0))
% 28.68/28.87 (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t133 t134))
% 28.68/28.87 (step t136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t135 t136))
% 28.68/28.87 (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t137))
% 28.68/28.87 (step t139 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t138))
% 28.68/28.87 (step t140 (cl (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t139 a5))
% 28.68/28.87 (step t141 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t132 a8 t140))
% 28.68/28.87 (step t142 (cl (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule and_neg)
% 28.68/28.87 (step t143 (cl (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t144)
% 28.68/28.87 (assume t144.a0 (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (assume t144.a1 (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t144.t1 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t144.t2)
% 28.68/28.87 (assume t144.t2.a0 (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (assume t144.t2.a1 (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t144.t2.t1 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule equiv_simplify)
% 28.68/28.87 (step t144.t2.t2 (cl (not (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true)) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule equiv1 :premises (t144.t2.t1))
% 28.68/28.87 (step t144.t2.t3 (cl (= (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule symm :premises (t144.t2.a1))
% 28.68/28.87 (step t144.t2.t4 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule cong :premises (t144.t2.t3))
% 28.68/28.87 (step t144.t2.t5 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule equiv_simplify)
% 28.68/28.87 (step t144.t2.t6 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule equiv2 :premises (t144.t2.t5))
% 28.68/28.87 (step t144.t2.t7 (cl (= (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true)) :rule resolution :premises (t144.t2.t6 t144.t2.a0))
% 28.68/28.87 (step t144.t2.t8 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) true)) :rule trans :premises (t144.t2.t4 t144.t2.t7))
% 28.68/28.87 (step t144.t2.t9 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t144.t2.t2 t144.t2.t8))
% 28.68/28.87 (step t144.t2 (cl (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t144.t2.a0 t144.t2.a1))
% 28.68/28.87 (step t144.t3 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t144.t4 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t144.t5 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t144.t2 t144.t3 t144.t4))
% 28.68/28.87 (step t144.t6 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule reordering :premises (t144.t5))
% 28.68/28.87 (step t144.t7 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule contraction :premises (t144.t6))
% 28.68/28.87 (step t144.t8 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t144.t1 t144.t7))
% 28.68/28.87 (step t144.t9 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t144.t10 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t144.t8 t144.t9))
% 28.68/28.87 (step t144.t11 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t144.t10))
% 28.68/28.87 (step t144.t12 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t144.t11))
% 28.68/28.87 (step t144.t13 (cl (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule and_neg)
% 28.68/28.87 (step t144.t14 (cl (and (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t144.t13 t144.a1 t144.a0))
% 28.68/28.87 (step t144.t15 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t144.t12 t144.t14))
% 28.68/28.87 (step t144 (cl (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t144.a0 t144.a1))
% 28.68/28.87 (step t145 (cl (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t146 (cl (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t147 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t144 t145 t146))
% 28.68/28.87 (step t148 (cl (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule reordering :premises (t147))
% 28.68/28.87 (step t149 (cl (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule contraction :premises (t148))
% 28.68/28.87 (step t150 (cl (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t143 t149))
% 28.68/28.87 (step t151 (cl (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t152 (cl (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t150 t151))
% 28.68/28.87 (step t153 (cl (=> (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t152))
% 28.68/28.87 (step t154 (cl (not (and (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t153))
% 28.68/28.87 (step t155 (cl (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t142 t154))
% 28.68/28.87 (step t156 (cl (not (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule reordering :premises (t155))
% 28.68/28.87 (step t157 (cl (not (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule or_pos)
% 28.68/28.87 (step t158 (cl (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule reordering :premises (t157))
% 28.68/28.87 (step t159 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t160)
% 28.68/28.87 (assume t160.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 28.68/28.87 (step t160.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule forall_inst :args ((:= A tptp.q) (:= B tptp.r) (:= C tptp.p)))
% 28.68/28.87 (step t160.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule or :premises (t160.t1))
% 28.68/28.87 (step t160.t3 (cl (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t160.t2 t160.a0))
% 28.68/28.87 (step t160 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t160.a0))
% 28.68/28.87 (step t161 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t159 t160))
% 28.68/28.87 (step t162 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t163 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t161 t162))
% 28.68/28.87 (step t164 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t163))
% 28.68/28.87 (step t165 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t164))
% 28.68/28.87 (step t166 (cl (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t165 a4))
% 28.68/28.87 (step t167 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t168)
% 28.68/28.87 (assume t168.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.87 (step t168.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t168.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule or :premises (t168.t1))
% 28.68/28.87 (step t168.t3 (cl (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t168.t2 t168.a0))
% 28.68/28.87 (step t168 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t168.a0))
% 28.68/28.87 (step t169 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t167 t168))
% 28.68/28.87 (step t170 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (not (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.87 (step t171 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t169 t170))
% 28.68/28.87 (step t172 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t171))
% 28.68/28.87 (step t173 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule implies :premises (t172))
% 28.68/28.87 (step t174 (cl (or (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (not (tptp.axiom (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t173 a6))
% 28.68/28.87 (step t175 (cl (tptp.theorem (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t158 t166 t174))
% 28.68/28.87 (step t176 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t177)
% 28.68/28.87 (assume t177.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t177.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.q tptp.r)) (:= Y (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t177.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule or :premises (t177.t1))
% 28.68/28.87 (step t177.t3 (cl (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t177.t2 t177.a0))
% 28.68/28.87 (step t177 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t177.a0))
% 28.68/28.87 (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t176 t177))
% 28.68/28.87 (step t179 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t178 t179))
% 28.68/28.87 (step t181 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t180))
% 28.68/28.87 (step t182 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t181))
% 28.68/28.87 (step t183 (cl (= (tptp.implies (tptp.implies tptp.q tptp.r) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t182 a5))
% 28.68/28.87 (step t184 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t156 t175 t183))
% 28.68/28.87 (step t185 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t186)
% 28.68/28.87 (assume t186.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 28.68/28.87 (step t186.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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (:= Y (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t186.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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule or :premises (t186.t1))
% 28.68/28.87 (step t186.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t186.t2 t186.a0))
% 28.68/28.87 (step t186 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t186.a0))
% 28.68/28.87 (step t187 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t185 t186))
% 28.68/28.87 (step t188 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.87 (step t189 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) (=> (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t187 t188))
% 28.68/28.87 (step t190 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t189))
% 28.68/28.87 (step t191 (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.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule implies :premises (t190))
% 28.68/28.87 (step t192 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t191 a7))
% 28.68/28.87 (step t193 (cl (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t97 t141 t184 t192))
% 28.68/28.87 (step t194 (cl (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule or_pos)
% 28.68/28.87 (step t195 (cl (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule reordering :premises (t194))
% 28.68/28.87 (step t196 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t197)
% 28.68/28.87 (assume t197.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 28.68/28.87 (step t197.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule forall_inst :args ((:= A (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (:= B (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (:= C (tptp.not (tptp.implies tptp.q tptp.r)))))
% 28.68/28.87 (step t197.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule or :premises (t197.t1))
% 28.68/28.87 (step t197.t3 (cl (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t197.t2 t197.a0))
% 28.68/28.87 (step t197 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t197.a0))
% 28.68/28.87 (step t198 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t196 t197))
% 28.68/28.87 (step t199 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.87 (step t200 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t198 t199))
% 28.68/28.87 (step t201 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t200))
% 28.68/28.87 (step t202 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule implies :premises (t201))
% 28.68/28.87 (step t203 (cl (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t202 a4))
% 28.68/28.87 (step t204 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t205)
% 28.68/28.87 (assume t205.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.87 (step t205.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))
% 28.68/28.87 (step t205.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule or :premises (t205.t1))
% 28.68/28.87 (step t205.t3 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t205.t2 t205.a0))
% 28.68/28.87 (step t205 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule subproof :discharge (t205.a0))
% 28.68/28.87 (step t206 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t204 t205))
% 28.68/28.87 (step t207 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule implies_neg2)
% 28.68/28.87 (step t208 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule resolution :premises (t206 t207))
% 28.68/28.87 (step t209 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))))) :rule contraction :premises (t208))
% 28.68/28.87 (step t210 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule implies :premises (t209))
% 28.68/28.87 (step t211 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t210 a6))
% 28.68/28.87 (step t212 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t195 t203 t211))
% 28.68/28.87 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t214)
% 28.68/28.87 (assume t214.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 28.68/28.87 (step t214.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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (:= Y (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t214.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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule or :premises (t214.t1))
% 28.68/28.87 (step t214.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t214.t2 t214.a0))
% 28.68/28.87 (step t214 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t214.a0))
% 28.68/28.87 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t213 t214))
% 28.68/28.87 (step t216 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.87 (step t217 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t215 t216))
% 28.68/28.87 (step t218 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t217))
% 28.68/28.87 (step t219 (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.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule implies :premises (t218))
% 28.68/28.87 (step t220 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies tptp.q tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t219 a7))
% 28.68/28.87 (step t221 (cl (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t95 t193 t212 t220))
% 28.68/28.87 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t223)
% 28.68/28.87 (assume t223.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 28.68/28.87 (step t223.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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (:= Y (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))
% 28.68/28.87 (step t223.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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule or :premises (t223.t1))
% 28.68/28.87 (step t223.t3 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t223.t2 t223.a0))
% 28.68/28.87 (step t223 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule subproof :discharge (t223.a0))
% 28.68/28.87 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t222 t223))
% 28.68/28.87 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule implies_neg2)
% 28.68/28.87 (step t226 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule resolution :premises (t224 t225))
% 28.68/28.87 (step t227 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q))))))) :rule contraction :premises (t226))
% 28.68/28.87 (step t228 (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.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule implies :premises (t227))
% 28.68/28.87 (step t229 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)))))) :rule resolution :premises (t228 a7))
% 28.68/28.87 (step t230 (cl (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t74 t93 t221 t229))
% 28.68/28.87 (step t231 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule or_pos)
% 28.68/28.87 (step t232 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule reordering :premises (t231))
% 28.68/28.87 (step t233 (cl (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule or_pos)
% 28.68/28.87 (step t234 (cl (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))))) :rule reordering :premises (t233))
% 28.68/28.87 (step t235 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (forall ((A $$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)
% 28.68/28.87 (anchor :step t236)
% 28.68/28.87 (assume t236.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))))
% 28.68/28.87 (step t236.t1 (cl (or (not (forall ((A $$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.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)))) (:= B (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (:= C (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t236.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule or :premises (t236.t1))
% 28.68/28.87 (step t236.t3 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t236.t2 t236.a0))
% 28.68/28.87 (step t236 (cl (not (forall ((A $$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.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule subproof :discharge (t236.a0))
% 28.68/28.87 (step t237 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t235 t236))
% 28.68/28.87 (step t238 (cl (=> (forall ((A $$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.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule implies_neg2)
% 28.68/28.87 (step t239 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (=> (forall ((A $$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.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t237 t238))
% 28.68/28.87 (step t240 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule contraction :premises (t239))
% 28.68/28.87 (step t241 (cl (not (forall ((A $$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.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies :premises (t240))
% 28.68/28.87 (step t242 (cl (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t241 a3))
% 28.68/28.87 (step t243 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t244)
% 28.68/28.87 (assume t244.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.87 (step t244.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))
% 28.68/28.87 (step t244.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.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule or :premises (t244.t1))
% 28.68/28.87 (step t244.t3 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t244.t2 t244.a0))
% 28.68/28.87 (step t244 (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.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule subproof :discharge (t244.a0))
% 28.68/28.87 (step t245 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t243 t244))
% 28.68/28.87 (step t246 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (not (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))))) :rule implies_neg2)
% 28.68/28.87 (step t247 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))))) :rule resolution :premises (t245 t246))
% 28.68/28.87 (step t248 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))))) :rule contraction :premises (t247))
% 28.68/28.87 (step t249 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule implies :premises (t248))
% 28.68/28.87 (step t250 (cl (or (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t249 a6))
% 28.68/28.87 (step t251 (cl (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t234 t242 t250))
% 28.68/28.87 (step t252 (cl (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule and_neg)
% 28.68/28.87 (step t253 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t254)
% 28.68/28.87 (assume t254.a0 (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (assume t254.a1 (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (assume t254.a2 (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t254.t1 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t254.t2)
% 28.68/28.87 (assume t254.t2.a0 (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (assume t254.t2.a1 (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (assume t254.t2.a2 (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t254.t2.t1 (cl (= (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.87 (step t254.t2.t2 (cl (not (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true)) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule equiv1 :premises (t254.t2.t1))
% 28.68/28.87 (step t254.t2.t3 (cl (= (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))))) :rule refl)
% 28.68/28.87 (step t254.t2.t4 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule symm :premises (t254.t2.a2))
% 28.68/28.87 (step t254.t2.t5 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule cong :premises (t254.t2.t3 t254.t2.t4))
% 28.68/28.87 (step t254.t2.t6 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule symm :premises (t254.t2.a1))
% 28.68/28.87 (step t254.t2.t7 (cl (= (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule trans :premises (t254.t2.t5 t254.t2.t6))
% 28.68/28.87 (step t254.t2.t8 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule cong :premises (t254.t2.t7))
% 28.68/28.87 (step t254.t2.t9 (cl (= (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv_simplify)
% 28.68/28.87 (step t254.t2.t10 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv2 :premises (t254.t2.t9))
% 28.68/28.87 (step t254.t2.t11 (cl (= (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true)) :rule resolution :premises (t254.t2.t10 t254.t2.a0))
% 28.68/28.87 (step t254.t2.t12 (cl (= (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) true)) :rule trans :premises (t254.t2.t8 t254.t2.t11))
% 28.68/28.87 (step t254.t2.t13 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t254.t2.t2 t254.t2.t12))
% 28.68/28.87 (step t254.t2 (cl (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t254.t2.a0 t254.t2.a1 t254.t2.a2))
% 28.68/28.87 (step t254.t3 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t254.t4 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t254.t5 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t254.t6 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t254.t2 t254.t3 t254.t4 t254.t5))
% 28.68/28.87 (step t254.t7 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule reordering :premises (t254.t6))
% 28.68/28.87 (step t254.t8 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t254.t7))
% 28.68/28.87 (step t254.t9 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t254.t1 t254.t8))
% 28.68/28.87 (step t254.t10 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t254.t11 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t254.t9 t254.t10))
% 28.68/28.87 (step t254.t12 (cl (=> (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t254.t11))
% 28.68/28.87 (step t254.t13 (cl (not (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t254.t12))
% 28.68/28.87 (step t254.t14 (cl (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_neg)
% 28.68/28.87 (step t254.t15 (cl (and (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t254.t14 t254.a2 t254.a1 t254.a0))
% 28.68/28.87 (step t254.t16 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t254.t13 t254.t15))
% 28.68/28.87 (step t254 (cl (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t254.a0 t254.a1 t254.a2))
% 28.68/28.87 (step t255 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule and_pos)
% 28.68/28.87 (step t256 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t257 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule and_pos)
% 28.68/28.87 (step t258 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t254 t255 t256 t257))
% 28.68/28.87 (step t259 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule reordering :premises (t258))
% 28.68/28.87 (step t260 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t259))
% 28.68/28.87 (step t261 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t253 t260))
% 28.68/28.87 (step t262 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t263 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t261 t262))
% 28.68/28.87 (step t264 (cl (=> (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t263))
% 28.68/28.87 (step t265 (cl (not (and (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t264))
% 28.68/28.87 (step t266 (cl (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t252 t265))
% 28.68/28.87 (step t267 (cl (not (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule reordering :premises (t266))
% 28.68/28.87 (step t268 (cl (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule or_pos)
% 28.68/28.87 (step t269 (cl (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule reordering :premises (t268))
% 28.68/28.87 (step t270 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t271)
% 28.68/28.87 (assume t271.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 28.68/28.87 (step t271.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule forall_inst :args ((:= A (tptp.or tptp.p tptp.q)) (:= B (tptp.or tptp.p tptp.r)) (:= C (tptp.not (tptp.or tptp.q tptp.p)))))
% 28.68/28.87 (step t271.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule or :premises (t271.t1))
% 28.68/28.87 (step t271.t3 (cl (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t271.t2 t271.a0))
% 28.68/28.87 (step t271 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t271.a0))
% 28.68/28.87 (step t272 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t270 t271))
% 28.68/28.87 (step t273 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t274 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t272 t273))
% 28.68/28.87 (step t275 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t274))
% 28.68/28.87 (step t276 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B)))))) (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t275))
% 28.68/28.87 (step t277 (cl (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t276 a4))
% 28.68/28.87 (step t278 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t279)
% 28.68/28.87 (assume t279.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 28.68/28.87 (step t279.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))
% 28.68/28.87 (step t279.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule or :premises (t279.t1))
% 28.68/28.87 (step t279.t3 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t279.t2 t279.a0))
% 28.68/28.87 (step t279 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule subproof :discharge (t279.a0))
% 28.68/28.87 (step t280 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t278 t279))
% 28.68/28.87 (step t281 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (not (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule implies_neg2)
% 28.68/28.87 (step t282 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t280 t281))
% 28.68/28.87 (step t283 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule contraction :premises (t282))
% 28.68/28.87 (step t284 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule implies :premises (t283))
% 28.68/28.87 (step t285 (cl (or (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.axiom (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t284 a6))
% 28.68/28.87 (step t286 (cl (tptp.theorem (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t269 t277 t285))
% 28.68/28.87 (step t287 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t288)
% 28.68/28.87 (assume t288.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t288.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (:= Y (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t288.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule or :premises (t288.t1))
% 28.68/28.87 (step t288.t3 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t288.t2 t288.a0))
% 28.68/28.87 (step t288 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t288.a0))
% 28.68/28.87 (step t289 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t287 t288))
% 28.68/28.87 (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t291 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t289 t290))
% 28.68/28.87 (step t292 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t291))
% 28.68/28.87 (step t293 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t292))
% 28.68/28.87 (step t294 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t293 a5))
% 28.68/28.87 (step t295 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t296)
% 28.68/28.87 (assume t296.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t296.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (:= Y (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t296.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule or :premises (t296.t1))
% 28.68/28.87 (step t296.t3 (cl (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t296.t2 t296.a0))
% 28.68/28.87 (step t296 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t296.a0))
% 28.68/28.87 (step t297 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t295 t296))
% 28.68/28.87 (step t298 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t299 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t297 t298))
% 28.68/28.87 (step t300 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t299))
% 28.68/28.87 (step t301 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t300))
% 28.68/28.87 (step t302 (cl (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t301 a5))
% 28.68/28.87 (step t303 (cl (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t267 t286 t294 t302))
% 28.68/28.87 (step t304 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t305)
% 28.68/28.87 (assume t305.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 28.68/28.87 (step t305.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (:= Y (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))
% 28.68/28.87 (step t305.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule or :premises (t305.t1))
% 28.68/28.87 (step t305.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t305.t2 t305.a0))
% 28.68/28.87 (step t305 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule subproof :discharge (t305.a0))
% 28.68/28.87 (step t306 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t304 t305))
% 28.68/28.87 (step t307 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule implies_neg2)
% 28.68/28.87 (step t308 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (=> (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule resolution :premises (t306 t307))
% 28.68/28.87 (step t309 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))))) :rule contraction :premises (t308))
% 28.68/28.87 (step t310 (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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule implies :premises (t309))
% 28.68/28.87 (step t311 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (not (tptp.theorem (tptp.implies (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule resolution :premises (t310 a7))
% 28.68/28.87 (step t312 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t232 t251 t303 t311))
% 28.68/28.87 (step t313 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule equiv_pos2)
% 28.68/28.87 (step t314 (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)
% 28.68/28.87 (step t315 (cl (= (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule all_simplify)
% 28.68/28.87 (step t316 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))))) :rule cong :premises (t314 t315))
% 28.68/28.87 (step t317 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t318)
% 28.68/28.87 (assume t318.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t318.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (:= Y (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))
% 28.68/28.87 (step t318.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.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule or :premises (t318.t1))
% 28.68/28.87 (step t318.t3 (cl (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t318.t2 t318.a0))
% 28.68/28.87 (step t318 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule subproof :discharge (t318.a0))
% 28.68/28.87 (step t319 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t317 t318))
% 28.68/28.87 (step t320 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (not (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule implies_neg2)
% 28.68/28.87 (step t321 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t319 t320))
% 28.68/28.87 (step t322 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule contraction :premises (t321))
% 28.68/28.87 (step t323 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))))) :rule resolution :premises (t313 t316 t322))
% 28.68/28.87 (step t324 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule implies :premises (t323))
% 28.68/28.87 (step t325 (cl (= (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (tptp.implies (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t324 a5))
% 28.68/28.87 (step t326 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t327)
% 28.68/28.87 (assume t327.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t327.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (:= Y (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))
% 28.68/28.87 (step t327.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule or :premises (t327.t1))
% 28.68/28.87 (step t327.t3 (cl (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t327.t2 t327.a0))
% 28.68/28.87 (step t327 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule subproof :discharge (t327.a0))
% 28.68/28.87 (step t328 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t326 t327))
% 28.68/28.87 (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (not (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule implies_neg2)
% 28.68/28.87 (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule resolution :premises (t328 t329))
% 28.68/28.87 (step t331 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)))))) :rule contraction :premises (t330))
% 28.68/28.87 (step t332 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule implies :premises (t331))
% 28.68/28.87 (step t333 (cl (= (tptp.implies (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r)) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))) (tptp.or (tptp.not (tptp.implies (tptp.or tptp.p tptp.q) (tptp.or tptp.p tptp.r))) (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t332 a5))
% 28.68/28.87 (step t334 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t335)
% 28.68/28.87 (assume t335.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t335.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))) :rule forall_inst :args ((:= X (tptp.or tptp.q tptp.p)) (:= Y (tptp.or tptp.p tptp.q))))
% 28.68/28.87 (step t335.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule or :premises (t335.t1))
% 28.68/28.87 (step t335.t3 (cl (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t335.t2 t335.a0))
% 28.68/28.87 (step t335 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule subproof :discharge (t335.a0))
% 28.68/28.87 (step t336 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t334 t335))
% 28.68/28.87 (step t337 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))) :rule implies_neg2)
% 28.68/28.87 (step t338 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))) :rule resolution :premises (t336 t337))
% 28.68/28.87 (step t339 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q))))) :rule contraction :premises (t338))
% 28.68/28.87 (step t340 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule implies :premises (t339))
% 28.68/28.87 (step t341 (cl (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.q)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.q)))) :rule resolution :premises (t340 a5))
% 28.68/28.87 (step t342 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) :rule implies_neg1)
% 28.68/28.87 (anchor :step t343)
% 28.68/28.87 (assume t343.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 28.68/28.87 (step t343.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule forall_inst :args ((:= X (tptp.or tptp.q tptp.p)) (:= Y (tptp.or tptp.p tptp.r))))
% 28.68/28.87 (step t343.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule or :premises (t343.t1))
% 28.68/28.87 (step t343.t3 (cl (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule resolution :premises (t343.t2 t343.a0))
% 28.68/28.87 (step t343 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule subproof :discharge (t343.a0))
% 28.68/28.87 (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule resolution :premises (t342 t343))
% 28.68/28.87 (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (not (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule implies_neg2)
% 28.68/28.87 (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule resolution :premises (t344 t345))
% 28.68/28.87 (step t347 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r))))) :rule contraction :premises (t346))
% 28.68/28.87 (step t348 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y)))) (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule implies :premises (t347))
% 28.68/28.87 (step t349 (cl (= (tptp.implies (tptp.or tptp.q tptp.p) (tptp.or tptp.p tptp.r)) (tptp.or (tptp.not (tptp.or tptp.q tptp.p)) (tptp.or tptp.p tptp.r)))) :rule resolution :premises (t348 a5))
% 28.68/28.87 (step t350 (cl) :rule resolution :premises (t72 t230 t312 t325 t333 t341 t349))
% 28.68/28.87
% 28.68/28.88 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.NiWy94TbTR/cvc5---1.0.5_3503.smt2
% 28.68/28.88 % cvc5---1.0.5 exiting
% 28.68/28.88 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------