TSTP Solution File: LCL287-3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL287-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:25:05 EDT 2024
% Result : Unsatisfiable 103.88s 104.32s
% Output : Proof 103.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.17 % Problem : LCL287-3 : TPTP v8.2.0. Released v2.3.0.
% 0.18/0.18 % Command : do_cvc5 %s %d
% 0.18/0.40 % Computer : n025.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Mon May 27 18:40:09 EDT 2024
% 0.18/0.40 % CPUTime :
% 0.38/0.56 %----Proving TF0_NAR, FOF, or CNF
% 0.38/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.58/10.83 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.60/15.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.69/20.95 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.67/26.02 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.84/31.16 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.86/36.21 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.08/41.47 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.19/46.64 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.38/51.81 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.45/56.88 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.56/62.01 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 66.63/67.09 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 76.74/77.25 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 86.93/87.41 --- Run --no-cbqi --full-saturate-quant at 10...
% 97.08/97.54 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 103.88/104.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.seuBCrjZ0g/cvc5---1.0.5_23482.smt2
% 103.88/104.32 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.seuBCrjZ0g/cvc5---1.0.5_23482.smt2
% 103.88/104.34 (assume a0 (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))))
% 103.88/104.34 (assume a1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))))
% 103.88/104.34 (assume a2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))))
% 103.88/104.34 (assume a3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))))
% 103.88/104.34 (assume a4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.implies A B) (tptp.implies (tptp.or C A) (tptp.or C B))))))
% 103.88/104.34 (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.or (tptp.not X) Y))))
% 103.88/104.34 (assume a6 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.34 (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))))
% 103.88/104.34 (assume a8 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.and P Q) (tptp.not (tptp.or (tptp.not P) (tptp.not Q))))))
% 103.88/104.34 (assume a9 (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))))
% 103.88/104.34 (assume a10 (not (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))
% 103.88/104.34 (step t1 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 103.88/104.34 (anchor :step t2)
% 103.88/104.34 (assume t2.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.34 (step t2.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.34 (step t2.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or :premises (t2.t1))
% 103.88/104.34 (step t2.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t2.t2 t2.a0))
% 103.88/104.34 (step t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule subproof :discharge (t2.a0))
% 103.88/104.34 (step t3 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t1 t2))
% 103.88/104.34 (step t4 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies_neg2)
% 103.88/104.34 (step t5 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t3 t4))
% 103.88/104.34 (step t6 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule contraction :premises (t5))
% 103.88/104.34 (step t7 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies :premises (t6))
% 103.88/104.34 (step t8 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or_pos)
% 103.88/104.34 (step t9 (cl (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule reordering :premises (t8))
% 103.88/104.34 (step t10 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or_pos)
% 103.88/104.34 (step t11 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule reordering :premises (t10))
% 103.88/104.34 (step t12 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or_pos)
% 103.88/104.34 (step t13 (cl (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule reordering :premises (t12))
% 103.88/104.34 (step t14 (cl (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule or_pos)
% 103.88/104.34 (step t15 (cl (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule reordering :premises (t14))
% 103.88/104.34 (step t16 (cl (not (= (not (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (not (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule equiv_pos2)
% 103.88/104.34 (step t17 (cl (and (= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731)))))) (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703))))) (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) (not (= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))))) (not (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) (not (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681))))) :rule and_neg)
% 103.88/104.34 (step t18 (cl (not (= (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P)))))))) (not (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P))))))) :rule equiv_pos2)
% 103.88/104.34 (anchor :step t19 :args ((P $$unsorted) (:= P P) (Q $$unsorted) (:= Q Q)))
% 103.88/104.34 (step t19.t1 (cl (= P P)) :rule refl)
% 103.88/104.34 (step t19.t2 (cl (= Q Q)) :rule refl)
% 103.88/104.34 (step t19.t3 (cl (= (tptp.equivalent P Q) (tptp.equivalent P Q))) :rule refl)
% 103.88/104.34 (step t19.t4 (cl (and (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703))))) (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) (not (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) (not (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681))))) :rule and_neg)
% 103.88/104.34 (step t19.t5 (cl (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) :rule hole :premises (a8) :args ((= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))))
% 103.88/104.34 (step t19.t6 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule hole :premises (a5) :args ((= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))))
% 103.88/104.34 (step t19.t7 (cl (and (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703))))) (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681))))) :rule resolution :premises (t19.t4 t19.t5 t19.t6))
% 103.88/104.34 (step t19.t8 (cl (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) :rule and :premises (t19.t7))
% 103.88/104.34 (step t19.t9 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule and :premises (t19.t7))
% 103.88/104.34 (step t19.t10 (cl (= P P)) :rule refl)
% 103.88/104.34 (step t19.t11 (cl (= Q Q)) :rule refl)
% 103.88/104.34 (step t19.t12 (cl (= (tptp.implies P Q) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q))) :rule hole :premises (t19.t9 t19.t10 t19.t11) :args (24))
% 103.88/104.34 (step t19.t13 (cl (= (tptp.implies Q P) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P))) :rule hole :premises (t19.t9 t19.t11 t19.t10) :args (24))
% 103.88/104.34 (step t19.t14 (cl (= (tptp.and (tptp.implies P Q) (tptp.implies Q P)) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P)))) :rule hole :premises (t19.t8 t19.t12 t19.t13) :args (24))
% 103.88/104.34 (step t19.t15 (cl (= (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P))) (= (tptp.equivalent P Q) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P))))) :rule cong :premises (t19.t3 t19.t14))
% 103.88/104.34 (step t19 (cl (= (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P)))))) :rule bind)
% 103.88/104.34 (anchor :step t20 :args ((P $$unsorted) (:= P P) (Q $$unsorted) (:= Q Q)))
% 103.88/104.34 (step t20.t1 (cl (= P P)) :rule refl)
% 103.88/104.34 (step t20.t2 (cl (= Q Q)) :rule refl)
% 103.88/104.34 (step t20.t3 (cl (= (tptp.equivalent P Q) (tptp.equivalent P Q))) :rule refl)
% 103.88/104.34 (step t20.t4 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q) (tptp.or (tptp.not P) Q))) :rule all_simplify)
% 103.88/104.34 (step t20.t5 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P) (tptp.or (tptp.not Q) P))) :rule all_simplify)
% 103.88/104.34 (step t20.t6 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P)) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (tptp.or (tptp.not P) Q)) (tptp.or (tptp.not Q) P)))) :rule cong :premises (t20.t4 t20.t5))
% 103.88/104.34 (step t20.t7 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (tptp.or (tptp.not P) Q)) (tptp.or (tptp.not Q) P)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P)))))) :rule all_simplify)
% 103.88/104.34 (step t20.t8 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P)))))) :rule trans :premises (t20.t6 t20.t7))
% 103.88/104.34 (step t20.t9 (cl (= (= (tptp.equivalent P Q) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P))) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P))))))) :rule cong :premises (t20.t3 t20.t8))
% 103.88/104.34 (step t20 (cl (= (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) P) Q)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Q) P)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P)))))))) :rule bind)
% 103.88/104.34 (step t21 (cl (= (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.and (tptp.implies P Q) (tptp.implies Q P)))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P)))))))) :rule trans :premises (t19 t20))
% 103.88/104.34 (step t22 (cl (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.equivalent P Q) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not P) Q)) (tptp.not (tptp.or (tptp.not Q) P))))))) :rule resolution :premises (t18 t21 a9))
% 103.88/104.34 (step t23 (cl (= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))))) :rule hole :premises (t22) :args ((= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))))))
% 103.88/104.34 (step t24 (cl (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) :rule hole :premises (a8) :args ((= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))))
% 103.88/104.34 (step t25 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule hole :premises (a5) :args ((= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))))
% 103.88/104.34 (step t26 (cl (and (= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731)))))) (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703))))) (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681))))) :rule resolution :premises (t17 t23 t24 t25))
% 103.88/104.34 (step t27 (cl (= tptp.equivalent (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))))) :rule and :premises (t26))
% 103.88/104.34 (step t28 (cl (= tptp.and (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))))) :rule and :premises (t26))
% 103.88/104.34 (step t29 (cl (= tptp.p tptp.p)) :rule refl)
% 103.88/104.34 (step t30 (cl (= tptp.q tptp.q)) :rule refl)
% 103.88/104.34 (step t31 (cl (= (tptp.and tptp.p tptp.q) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q))) :rule hole :premises (t28 t29 t30) :args (24))
% 103.88/104.34 (step t32 (cl (= (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) :rule refl)
% 103.88/104.34 (step t33 (cl (= (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) :rule hole :premises (t27 t31 t32) :args (24))
% 103.88/104.34 (step t34 (cl (= (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule cong :premises (t33))
% 103.88/104.34 (step t35 (cl (= (not (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule cong :premises (t34))
% 103.88/104.34 (step t36 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) :rule all_simplify)
% 103.88/104.34 (step t37 (cl (= (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) :rule refl)
% 103.88/104.34 (step t38 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) :rule cong :premises (t36 t37))
% 103.88/104.35 (step t39 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule all_simplify)
% 103.88/104.35 (step t40 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule trans :premises (t38 t39))
% 103.88/104.35 (step t41 (cl (= (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule cong :premises (t40))
% 103.88/104.35 (step t42 (cl (= (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_731 $$unsorted) (BOUND_VARIABLE_732 $$unsorted)) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_731) BOUND_VARIABLE_732)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_732) BOUND_VARIABLE_731))))) (@ (@ (lambda ((BOUND_VARIABLE_702 $$unsorted) (BOUND_VARIABLE_703 $$unsorted)) (tptp.not (tptp.or (tptp.not BOUND_VARIABLE_702) (tptp.not BOUND_VARIABLE_703)))) tptp.p) tptp.q)) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule cong :premises (t41))
% 103.88/104.35 (step t43 (cl (= (not (tptp.theorem (tptp.equivalent (tptp.and tptp.p tptp.q) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule trans :premises (t35 t42))
% 103.88/104.35 (step t44 (cl (not (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t16 t43 a10))
% 103.88/104.35 (step t45 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or_pos)
% 103.88/104.35 (step t46 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule reordering :premises (t45))
% 103.88/104.35 (step t47 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or_pos)
% 103.88/104.35 (step t48 (cl (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule reordering :premises (t47))
% 103.88/104.35 (step t49 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t50)
% 103.88/104.35 (assume t50.a0 (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))))
% 103.88/104.35 (step t50.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t50.t2 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or :premises (t50.t1))
% 103.88/104.35 (step t50.t3 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t50.t2 t50.a0))
% 103.88/104.35 (step t50 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule subproof :discharge (t50.a0))
% 103.88/104.35 (step t51 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t49 t50))
% 103.88/104.35 (step t52 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies_neg2)
% 103.88/104.35 (step t53 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t51 t52))
% 103.88/104.35 (step t54 (cl (=> (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule contraction :premises (t53))
% 103.88/104.35 (step t55 (cl (not (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule implies :premises (t54))
% 103.88/104.35 (step t56 (cl (not (= (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))))) (not (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A)))) (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) :rule equiv_pos2)
% 103.88/104.35 (anchor :step t57 :args ((A $$unsorted) (:= A A)))
% 103.88/104.35 (step t57.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t57.t2 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule and :premises (t26))
% 103.88/104.35 (step t57.t3 (cl (= (tptp.or A A) (tptp.or A A))) :rule refl)
% 103.88/104.35 (step t57.t4 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t57.t5 (cl (= (tptp.implies (tptp.or A A) A) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A))) :rule hole :premises (t57.t2 t57.t3 t57.t4) :args (24))
% 103.88/104.35 (step t57.t6 (cl (= (tptp.axiom (tptp.implies (tptp.or A A) A)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A)))) :rule cong :premises (t57.t5))
% 103.88/104.35 (step t57 (cl (= (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (forall ((A $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A))))) :rule bind)
% 103.88/104.35 (anchor :step t58 :args ((A $$unsorted) (:= A A)))
% 103.88/104.35 (step t58.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t58.t2 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A) (tptp.or (tptp.not (tptp.or A A)) A))) :rule all_simplify)
% 103.88/104.35 (step t58.t3 (cl (= (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) :rule cong :premises (t58.t2))
% 103.88/104.35 (step t58 (cl (= (forall ((A $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A A)) A))) (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))))) :rule bind)
% 103.88/104.35 (step t59 (cl (= (forall ((A $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A A) A))) (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A))))) :rule trans :premises (t57 t58))
% 103.88/104.35 (step t60 (cl (forall ((A $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A A)) A)))) :rule resolution :premises (t56 t59 a0))
% 103.88/104.35 (step t61 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t55 t60))
% 103.88/104.35 (step t62 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t63)
% 103.88/104.35 (assume t63.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.35 (step t63.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))
% 103.88/104.35 (step t63.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule or :premises (t63.t1))
% 103.88/104.35 (step t63.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t63.t2 t63.a0))
% 103.88/104.35 (step t63 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule subproof :discharge (t63.a0))
% 103.88/104.35 (step t64 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t62 t63))
% 103.88/104.35 (step t65 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule implies_neg2)
% 103.88/104.35 (step t66 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t64 t65))
% 103.88/104.35 (step t67 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule contraction :premises (t66))
% 103.88/104.35 (step t68 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies :premises (t67))
% 103.88/104.35 (step t69 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t68 a6))
% 103.88/104.35 (step t70 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t48 t61 t69))
% 103.88/104.35 (step t71 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))) :rule or_pos)
% 103.88/104.35 (step t72 (cl (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))))) :rule reordering :premises (t71))
% 103.88/104.35 (step t73 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t74)
% 103.88/104.35 (assume t74.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))))
% 103.88/104.35 (step t74.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (:= B (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t74.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule or :premises (t74.t1))
% 103.88/104.35 (step t74.t3 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t74.t2 t74.a0))
% 103.88/104.35 (step t74 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule subproof :discharge (t74.a0))
% 103.88/104.35 (step t75 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t73 t74))
% 103.88/104.35 (step t76 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))) :rule implies_neg2)
% 103.88/104.35 (step t77 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))) :rule resolution :premises (t75 t76))
% 103.88/104.35 (step t78 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))) :rule contraction :premises (t77))
% 103.88/104.35 (step t79 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule implies :premises (t78))
% 103.88/104.35 (step t80 (cl (not (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))))) (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) :rule equiv_pos2)
% 103.88/104.35 (anchor :step t81 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 103.88/104.35 (step t81.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t81.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t81.t3 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule and :premises (t26))
% 103.88/104.35 (step t81.t4 (cl (= (tptp.or A B) (tptp.or A B))) :rule refl)
% 103.88/104.35 (step t81.t5 (cl (= (tptp.or B A) (tptp.or B A))) :rule refl)
% 103.88/104.35 (step t81.t6 (cl (= (tptp.implies (tptp.or A B) (tptp.or B A)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A)))) :rule hole :premises (t81.t3 t81.t4 t81.t5) :args (24))
% 103.88/104.35 (step t81.t7 (cl (= (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A))) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A))))) :rule cong :premises (t81.t6))
% 103.88/104.35 (step t81 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A)))))) :rule bind)
% 103.88/104.35 (anchor :step t82 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 103.88/104.35 (step t82.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t82.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t82.t3 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A)) (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))) :rule all_simplify)
% 103.88/104.35 (step t82.t4 (cl (= (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A))) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) :rule cong :premises (t82.t3))
% 103.88/104.35 (step t82 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A B)) (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))))) :rule bind)
% 103.88/104.35 (step t83 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A B) (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A)))))) :rule trans :premises (t81 t82))
% 103.88/104.35 (step t84 (cl (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A B)) (tptp.or B A))))) :rule resolution :premises (t80 t83 a2))
% 103.88/104.35 (step t85 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t79 t84))
% 103.88/104.35 (step t86 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t87)
% 103.88/104.35 (assume t87.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.35 (step t87.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))
% 103.88/104.35 (step t87.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule or :premises (t87.t1))
% 103.88/104.35 (step t87.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule resolution :premises (t87.t2 t87.a0))
% 103.88/104.35 (step t87 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule subproof :discharge (t87.a0))
% 103.88/104.35 (step t88 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule resolution :premises (t86 t87))
% 103.88/104.35 (step t89 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))))) :rule implies_neg2)
% 103.88/104.35 (step t90 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))))) :rule resolution :premises (t88 t89))
% 103.88/104.35 (step t91 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))))))) :rule contraction :premises (t90))
% 103.88/104.35 (step t92 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule implies :premises (t91))
% 103.88/104.35 (step t93 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))))) :rule resolution :premises (t92 a6))
% 103.88/104.35 (step t94 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t72 t85 t93))
% 103.88/104.35 (step t95 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t96)
% 103.88/104.35 (assume t96.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))
% 103.88/104.35 (step t96.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (:= Y (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))
% 103.88/104.35 (step t96.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule or :premises (t96.t1))
% 103.88/104.35 (step t96.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t96.t2 t96.a0))
% 103.88/104.35 (step t96 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule subproof :discharge (t96.a0))
% 103.88/104.35 (step t97 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t95 t96))
% 103.88/104.35 (step t98 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule implies_neg2)
% 103.88/104.35 (step t99 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t97 t98))
% 103.88/104.35 (step t100 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule contraction :premises (t99))
% 103.88/104.35 (step t101 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies :premises (t100))
% 103.88/104.35 (step t102 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule equiv_pos2)
% 103.88/104.35 (anchor :step t103 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 103.88/104.35 (step t103.t1 (cl (= X X)) :rule refl)
% 103.88/104.35 (step t103.t2 (cl (= Y Y)) :rule refl)
% 103.88/104.35 (step t103.t3 (cl (= (tptp.theorem X) (tptp.theorem X))) :rule refl)
% 103.88/104.35 (step t103.t4 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule hole :premises (a5) :args ((= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))))
% 103.88/104.35 (step t103.t5 (cl (= Y Y)) :rule refl)
% 103.88/104.35 (step t103.t6 (cl (= X X)) :rule refl)
% 103.88/104.35 (step t103.t7 (cl (= (tptp.implies Y X) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) :rule hole :premises (t103.t4 t103.t5 t103.t6) :args (24))
% 103.88/104.35 (step t103.t8 (cl (= (tptp.theorem (tptp.implies Y X)) (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X)))) :rule cong :premises (t103.t7))
% 103.88/104.35 (step t103.t9 (cl (= (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))))) :rule cong :premises (t103.t8))
% 103.88/104.35 (step t103.t10 (cl (= (not (tptp.theorem Y)) (not (tptp.theorem Y)))) :rule refl)
% 103.88/104.35 (step t103.t11 (cl (= (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y))) (or (tptp.theorem X) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) (not (tptp.theorem Y))))) :rule cong :premises (t103.t3 t103.t9 t103.t10))
% 103.88/104.35 (step t103 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) (not (tptp.theorem Y)))))) :rule bind)
% 103.88/104.35 (anchor :step t104 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 103.88/104.35 (step t104.t1 (cl (= X X)) :rule refl)
% 103.88/104.35 (step t104.t2 (cl (= Y Y)) :rule refl)
% 103.88/104.35 (step t104.t3 (cl (= (tptp.theorem X) (tptp.theorem X))) :rule refl)
% 103.88/104.35 (step t104.t4 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X) (tptp.or (tptp.not Y) X))) :rule all_simplify)
% 103.88/104.35 (step t104.t5 (cl (= (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X)) (tptp.theorem (tptp.or (tptp.not Y) X)))) :rule cong :premises (t104.t4))
% 103.88/104.35 (step t104.t6 (cl (= (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) (not (tptp.theorem (tptp.or (tptp.not Y) X))))) :rule cong :premises (t104.t5))
% 103.88/104.35 (step t104.t7 (cl (= (not (tptp.theorem Y)) (not (tptp.theorem Y)))) :rule refl)
% 103.88/104.35 (step t104.t8 (cl (= (or (tptp.theorem X) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) (not (tptp.theorem Y))) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule cong :premises (t104.t3 t104.t6 t104.t7))
% 103.88/104.35 (step t104 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) Y) X))) (not (tptp.theorem Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))) :rule bind)
% 103.88/104.35 (step t105 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.implies Y X))) (not (tptp.theorem Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))) :rule trans :premises (t103 t104))
% 103.88/104.35 (step t106 (cl (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule resolution :premises (t102 t105 a7))
% 103.88/104.35 (step t107 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t101 t106))
% 103.88/104.35 (step t108 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t46 t70 t94 t107))
% 103.88/104.35 (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t110)
% 103.88/104.35 (assume t110.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))
% 103.88/104.35 (step t110.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule forall_inst :args ((:= X (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (:= Y (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))
% 103.88/104.35 (step t110.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or :premises (t110.t1))
% 103.88/104.35 (step t110.t3 (cl (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t110.t2 t110.a0))
% 103.88/104.35 (step t110 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule subproof :discharge (t110.a0))
% 103.88/104.35 (step t111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t109 t110))
% 103.88/104.35 (step t112 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies_neg2)
% 103.88/104.35 (step t113 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t111 t112))
% 103.88/104.35 (step t114 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule contraction :premises (t113))
% 103.88/104.35 (step t115 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule implies :premises (t114))
% 103.88/104.35 (step t116 (cl (or (tptp.theorem (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t115 t106))
% 103.88/104.35 (step t117 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t15 t44 t108 t116))
% 103.88/104.35 (step t118 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or_pos)
% 103.88/104.35 (step t119 (cl (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule reordering :premises (t118))
% 103.88/104.35 (step t120 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t121)
% 103.88/104.35 (assume t121.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))))
% 103.88/104.35 (step t121.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (:= B (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t121.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule or :premises (t121.t1))
% 103.88/104.35 (step t121.t3 (cl (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t121.t2 t121.a0))
% 103.88/104.35 (step t121 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule subproof :discharge (t121.a0))
% 103.88/104.35 (step t122 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t120 t121))
% 103.88/104.35 (step t123 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule implies_neg2)
% 103.88/104.35 (step t124 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t122 t123))
% 103.88/104.35 (step t125 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule contraction :premises (t124))
% 103.88/104.35 (step t126 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule implies :premises (t125))
% 103.88/104.35 (step t127 (cl (not (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))))) (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) :rule equiv_pos2)
% 103.88/104.35 (anchor :step t128 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 103.88/104.35 (step t128.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t128.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t128.t3 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule and :premises (t26))
% 103.88/104.35 (step t128.t4 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t128.t5 (cl (= (tptp.or B A) (tptp.or B A))) :rule refl)
% 103.88/104.35 (step t128.t6 (cl (= (tptp.implies A (tptp.or B A)) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A)))) :rule hole :premises (t128.t3 t128.t4 t128.t5) :args (24))
% 103.88/104.35 (step t128.t7 (cl (= (tptp.axiom (tptp.implies A (tptp.or B A))) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A))))) :rule cong :premises (t128.t6))
% 103.88/104.35 (step t128 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A)))))) :rule bind)
% 103.88/104.35 (anchor :step t129 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B)))
% 103.88/104.35 (step t129.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t129.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t129.t3 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A)) (tptp.or (tptp.not A) (tptp.or B A)))) :rule all_simplify)
% 103.88/104.35 (step t129.t4 (cl (= (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A))) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) :rule cong :premises (t129.t3))
% 103.88/104.35 (step t129 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) A) (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))))) :rule bind)
% 103.88/104.35 (step t130 (cl (= (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.implies A (tptp.or B A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))))) :rule trans :premises (t128 t129))
% 103.88/104.35 (step t131 (cl (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) :rule resolution :premises (t127 t130 a1))
% 103.88/104.35 (step t132 (cl (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t126 t131))
% 103.88/104.35 (step t133 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t134)
% 103.88/104.35 (assume t134.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.35 (step t134.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t134.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or :premises (t134.t1))
% 103.88/104.35 (step t134.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t134.t2 t134.a0))
% 103.88/104.35 (step t134 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule subproof :discharge (t134.a0))
% 103.88/104.35 (step t135 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t133 t134))
% 103.88/104.35 (step t136 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies_neg2)
% 103.88/104.35 (step t137 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t135 t136))
% 103.88/104.35 (step t138 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule contraction :premises (t137))
% 103.88/104.35 (step t139 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies :premises (t138))
% 103.88/104.35 (step t140 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t139 a6))
% 103.88/104.35 (step t141 (cl (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t119 t132 t140))
% 103.88/104.35 (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t143)
% 103.88/104.35 (assume t143.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))
% 103.88/104.35 (step t143.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (:= Y (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t143.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or :premises (t143.t1))
% 103.88/104.35 (step t143.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t143.t2 t143.a0))
% 103.88/104.35 (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule subproof :discharge (t143.a0))
% 103.88/104.35 (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t142 t143))
% 103.88/104.35 (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies_neg2)
% 103.88/104.35 (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t144 t145))
% 103.88/104.35 (step t147 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule contraction :premises (t146))
% 103.88/104.35 (step t148 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies :premises (t147))
% 103.88/104.35 (step t149 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t148 t106))
% 103.88/104.35 (step t150 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t13 t117 t141 t149))
% 103.88/104.35 (step t151 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or_pos)
% 103.88/104.35 (step t152 (cl (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule reordering :premises (t151))
% 103.88/104.35 (step t153 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t154)
% 103.88/104.35 (assume t154.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))))
% 103.88/104.35 (step t154.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (:= B (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (:= C (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))
% 103.88/104.35 (step t154.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule or :premises (t154.t1))
% 103.88/104.35 (step t154.t3 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t154.t2 t154.a0))
% 103.88/104.35 (step t154 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule subproof :discharge (t154.a0))
% 103.88/104.35 (step t155 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t153 t154))
% 103.88/104.35 (step t156 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies_neg2)
% 103.88/104.35 (step t157 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t155 t156))
% 103.88/104.35 (step t158 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule contraction :premises (t157))
% 103.88/104.35 (step t159 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule implies :premises (t158))
% 103.88/104.35 (step t160 (cl (not (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) :rule equiv_pos2)
% 103.88/104.35 (anchor :step t161 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (C $$unsorted) (:= C C)))
% 103.88/104.35 (step t161.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t161.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t161.t3 (cl (= C C)) :rule refl)
% 103.88/104.35 (step t161.t4 (cl (= tptp.implies (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)))) :rule and :premises (t26))
% 103.88/104.35 (step t161.t5 (cl (= (tptp.or A (tptp.or B C)) (tptp.or A (tptp.or B C)))) :rule refl)
% 103.88/104.35 (step t161.t6 (cl (= (tptp.or B (tptp.or A C)) (tptp.or B (tptp.or A C)))) :rule refl)
% 103.88/104.35 (step t161.t7 (cl (= (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))) (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) :rule hole :premises (t161.t4 t161.t5 t161.t6) :args (24))
% 103.88/104.35 (step t161.t8 (cl (= (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C)))) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) :rule cong :premises (t161.t7))
% 103.88/104.35 (step t161 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))))) :rule bind)
% 103.88/104.35 (anchor :step t162 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (C $$unsorted) (:= C C)))
% 103.88/104.35 (step t162.t1 (cl (= A A)) :rule refl)
% 103.88/104.35 (step t162.t2 (cl (= B B)) :rule refl)
% 103.88/104.35 (step t162.t3 (cl (= C C)) :rule refl)
% 103.88/104.35 (step t162.t4 (cl (= (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))) (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) :rule all_simplify)
% 103.88/104.35 (step t162.t5 (cl (= (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) :rule cong :premises (t162.t4))
% 103.88/104.35 (step t162 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (@ (@ (lambda ((BOUND_VARIABLE_680 $$unsorted) (BOUND_VARIABLE_681 $$unsorted)) (tptp.or (tptp.not BOUND_VARIABLE_680) BOUND_VARIABLE_681)) (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))))) :rule bind)
% 103.88/104.35 (step t163 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.implies (tptp.or A (tptp.or B C)) (tptp.or B (tptp.or A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C))))))) :rule trans :premises (t161 t162))
% 103.88/104.35 (step t164 (cl (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.axiom (tptp.or (tptp.not (tptp.or A (tptp.or B C))) (tptp.or B (tptp.or A C)))))) :rule resolution :premises (t160 t163 a3))
% 103.88/104.35 (step t165 (cl (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t159 t164))
% 103.88/104.35 (step t166 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t167)
% 103.88/104.35 (assume t167.a0 (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))))
% 103.88/104.35 (step t167.t1 (cl (or (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))
% 103.88/104.35 (step t167.t2 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule or :premises (t167.t1))
% 103.88/104.35 (step t167.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t167.t2 t167.a0))
% 103.88/104.35 (step t167 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule subproof :discharge (t167.a0))
% 103.88/104.35 (step t168 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t166 t167))
% 103.88/104.35 (step t169 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule implies_neg2)
% 103.88/104.35 (step t170 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule resolution :premises (t168 t169))
% 103.88/104.35 (step t171 (cl (=> (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))))) :rule contraction :premises (t170))
% 103.88/104.35 (step t172 (cl (not (forall ((X $$unsorted)) (or (tptp.theorem X) (not (tptp.axiom X))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies :premises (t171))
% 103.88/104.35 (step t173 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t172 a6))
% 103.88/104.35 (step t174 (cl (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t152 t165 t173))
% 103.88/104.35 (step t175 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t176)
% 103.88/104.35 (assume t176.a0 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))))
% 103.88/104.35 (step t176.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule forall_inst :args ((:= X (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (:= Y (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))
% 103.88/104.35 (step t176.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule or :premises (t176.t1))
% 103.88/104.35 (step t176.t3 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t176.t2 t176.a0))
% 103.88/104.35 (step t176 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule subproof :discharge (t176.a0))
% 103.88/104.35 (step t177 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t175 t176))
% 103.88/104.35 (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (not (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule implies_neg2)
% 103.88/104.35 (step t179 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t177 t178))
% 103.88/104.35 (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y)))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule contraction :premises (t179))
% 103.88/104.35 (step t181 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.theorem X) (not (tptp.theorem (tptp.or (tptp.not Y) X))) (not (tptp.theorem Y))))) (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule implies :premises (t180))
% 103.88/104.35 (step t182 (cl (or (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))))) :rule resolution :premises (t181 t106))
% 103.88/104.35 (step t183 (cl (not (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t11 t150 t174 t182))
% 103.88/104.35 (step t184 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) :rule implies_neg1)
% 103.88/104.35 (anchor :step t185)
% 103.88/104.35 (assume t185.a0 (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))))
% 103.88/104.35 (step t185.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule forall_inst :args ((:= A (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (:= B (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))
% 103.88/104.35 (step t185.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule or :premises (t185.t1))
% 103.88/104.35 (step t185.t3 (cl (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t185.t2 t185.a0))
% 103.88/104.35 (step t185 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule subproof :discharge (t185.a0))
% 103.88/104.35 (step t186 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t184 t185))
% 103.88/104.35 (step t187 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule implies_neg2)
% 103.88/104.35 (step t188 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule resolution :premises (t186 t187))
% 103.88/104.35 (step t189 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A)))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))) :rule contraction :premises (t188))
% 103.88/104.35 (step t190 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (tptp.axiom (tptp.or (tptp.not A) (tptp.or B A))))) (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule implies :premises (t189))
% 103.88/104.35 (step t191 (cl (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))))) :rule resolution :premises (t190 t131))
% 103.88/104.35 (step t192 (cl (not (or (tptp.theorem (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (not (tptp.axiom (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.or (tptp.not (tptp.or (tptp.not (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))) (tptp.not (tptp.or (tptp.not tptp.p) (tptp.not tptp.q)))))))))) :rule resolution :premises (t9 t183 t191))
% 103.88/104.35 (step t193 (cl) :rule resolution :premises (t7 t192 a6))
% 103.88/104.35
% 103.88/104.35 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.seuBCrjZ0g/cvc5---1.0.5_23482.smt2
% 103.88/104.36 % cvc5---1.0.5 exiting
% 103.88/104.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------