%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN067-3 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:38:08 AM UTC 2025
% Result : Unsatisfiable 0.40s 0.58s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN067-3 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.40/0.58 % SZS status Unsatisfiable
% 0.40/0.58 % SZS output start Proof
% 0.40/0.58 tff(big_r_type, type, (
% 0.40/0.58 big_r: ( $i * $i ) > $o)).
% 0.40/0.58 tff(sk2_type, type, (
% 0.40/0.58 sk2: $i > $i)).
% 0.40/0.58 tff(sk9_type, type, (
% 0.40/0.58 sk9: $i)).
% 0.40/0.58 tff(big_p_type, type, (
% 0.40/0.58 big_p: $i > $o)).
% 0.40/0.58 tff(sk10_type, type, (
% 0.40/0.58 sk10: $i)).
% 0.40/0.58 tff(sk5_type, type, (
% 0.40/0.58 sk5: $i > $i)).
% 0.40/0.58 tff(sk7_type, type, (
% 0.40/0.58 sk7: $i)).
% 0.40/0.58 tff(sk1_type, type, (
% 0.40/0.58 sk1: $i > $i)).
% 0.40/0.58 tff(sk8_type, type, (
% 0.40/0.58 sk8: $i)).
% 0.40/0.58 tff(sk3_type, type, (
% 0.40/0.58 sk3: $i > $i)).
% 0.40/0.58 tff(a_type, type, (
% 0.40/0.58 a: $i)).
% 0.40/0.58 tff(sk4_type, type, (
% 0.40/0.58 sk4: $i > $i)).
% 0.40/0.58 tff(sk6_type, type, (
% 0.40/0.58 sk6: $i > $i)).
% 0.40/0.58 tff(1,assumption,(~big_p(sk5(sk7))), introduced(assumption)).
% 0.40/0.58 tff(2,assumption,(~big_p(sk8)), introduced(assumption)).
% 0.40/0.58 tff(3,assumption,(~big_r(sk9, sk2(sk9))), introduced(assumption)).
% 0.40/0.58 tff(4,assumption,(~big_p(sk7)), introduced(assumption)).
% 0.40/0.58 tff(5,assumption,(~big_p(sk9)), introduced(assumption)).
% 0.40/0.58 tff(6,assumption,(~big_p(sk1(sk7))), introduced(assumption)).
% 0.40/0.58 tff(7,plain,
% 0.40/0.58 (big_p(a) <=> big_p(a)),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(8,axiom,(big_p(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_37')).
% 0.40/0.58 tff(9,plain,
% 0.40/0.58 (big_p(a)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.40/0.58 tff(10,plain,
% 0.40/0.58 (^[B: $i, A: $i] : refl(((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(11,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[10])).
% 0.40/0.58 tff(12,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(13,plain,
% 0.40/0.58 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(A) | big_p(B)) | big_p(sk1(B))) <=> (big_p(sk1(B)) | big_p(B) | big_p(A))), ((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) <=> ((big_p(sk1(B)) | big_p(B) | big_p(A)) | big_p(sk3(A))))), rewrite(((big_p(sk1(B)) | big_p(B) | big_p(A)) | big_p(sk3(A))) <=> (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))), ((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) <=> (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)))), (((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) | (~big_p(a))) <=> ((big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) | (~big_p(a))))), rewrite(((big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))), (((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(14,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) | (~big_p(a))) <=> ![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[13])).
% 0.40/0.58 tff(15,axiom,(![B: $i, A: $i] : ((((big_p(A) | big_p(B)) | big_p(sk1(B))) | big_p(sk3(A))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_1')).
% 0.40/0.58 tff(16,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.40/0.58 tff(17,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.40/0.58 tff(18,plain,(
% 0.40/0.58 ![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(skolemize,[status(sab)],[17])).
% 0.40/0.58 tff(19,plain,
% 0.40/0.58 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.40/0.58 tff(20,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(21,plain,
% 0.40/0.58 (((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7)) <=> ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(22,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[21])).
% 0.40/0.58 tff(23,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[22, 20])).
% 0.40/0.58 tff(24,plain,
% 0.40/0.58 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(25,plain,
% 0.40/0.58 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.40/0.58 tff(26,plain,
% 0.40/0.58 (big_p(sk3(sk7)) | big_p(sk1(sk7))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[25, 19, 9, 4])).
% 0.40/0.58 tff(27,plain,
% 0.40/0.58 (big_p(sk3(sk7))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[26, 6])).
% 0.40/0.58 tff(28,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(29,plain,
% 0.40/0.58 (((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9)) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(30,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.40/0.58 tff(31,plain,
% 0.40/0.58 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[30, 28])).
% 0.40/0.58 tff(32,plain,
% 0.40/0.58 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(33,plain,
% 0.40/0.58 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.40/0.58 tff(34,plain,
% 0.40/0.58 (big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[33, 19, 9, 5, 4])).
% 0.40/0.58 tff(35,plain,
% 0.40/0.58 (big_p(sk3(sk9))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[34, 6])).
% 0.40/0.58 tff(36,plain,
% 0.40/0.58 (^[I: $i, J: $i] : refl(((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(37,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[36])).
% 0.40/0.58 tff(38,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(39,plain,
% 0.40/0.58 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_p(I) | big_p(J)) <=> (big_p(I) | big_p(J))), (((big_p(I) | big_p(J)) | big_r(I, sk4(I))) <=> ((big_p(I) | big_p(J)) | big_r(I, sk4(I))))), rewrite(((big_p(I) | big_p(J)) | big_r(I, sk4(I))) <=> (big_p(I) | big_p(J) | big_r(I, sk4(I)))), (((big_p(I) | big_p(J)) | big_r(I, sk4(I))) <=> (big_p(I) | big_p(J) | big_r(I, sk4(I))))), ((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) <=> ((big_p(I) | big_p(J) | big_r(I, sk4(I))) | big_r(J, sk2(J))))), rewrite(((big_p(I) | big_p(J) | big_r(I, sk4(I))) | big_r(J, sk2(J))) <=> (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))), ((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) <=> (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))))), (((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) | (~big_p(a))) <=> ((big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) | (~big_p(a))))), rewrite(((big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))), (((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(40,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) | (~big_p(a))) <=> ![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[39])).
% 0.40/0.58 tff(41,axiom,(![I: $i, J: $i] : ((((big_p(I) | big_p(J)) | big_r(I, sk4(I))) | big_r(J, sk2(J))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_5')).
% 0.40/0.58 tff(42,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.40/0.58 tff(43,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.40/0.58 tff(44,plain,(
% 0.40/0.58 ![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(skolemize,[status(sab)],[43])).
% 0.40/0.58 tff(45,plain,
% 0.40/0.58 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.40/0.58 tff(46,plain,
% 0.40/0.58 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(47,plain,
% 0.40/0.58 (((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(48,plain,
% 0.40/0.58 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[47])).
% 0.40/0.59 tff(49,plain,
% 0.40/0.59 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[48, 46])).
% 0.40/0.59 tff(50,plain,
% 0.40/0.59 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(51,plain,
% 0.40/0.59 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.40/0.59 tff(52,plain,
% 0.40/0.59 (big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[51, 45, 9, 5])).
% 0.40/0.59 tff(53,plain,
% 0.40/0.59 (big_r(sk9, sk4(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[52, 3])).
% 0.40/0.59 tff(54,assumption,(~big_r(sk4(sk7), sk3(sk7))), introduced(assumption)).
% 0.40/0.59 tff(55,plain,
% 0.40/0.59 (^[E: $i, F: $i] : refl(((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(56,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[55])).
% 0.40/0.59 tff(57,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(58,plain,
% 0.40/0.59 (^[E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_p(E) | big_p(F)) <=> (big_p(E) | big_p(F))), (((big_p(E) | big_p(F)) | big_p(sk1(F))) <=> ((big_p(E) | big_p(F)) | big_p(sk1(F))))), rewrite(((big_p(E) | big_p(F)) | big_p(sk1(F))) <=> (big_p(E) | big_p(F) | big_p(sk1(F)))), (((big_p(E) | big_p(F)) | big_p(sk1(F))) <=> (big_p(E) | big_p(F) | big_p(sk1(F))))), ((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) <=> ((big_p(E) | big_p(F) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))))), rewrite(((big_p(E) | big_p(F) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) <=> (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))), ((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) <=> (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))))), (((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) | (~big_p(a))) <=> ((big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) | (~big_p(a))))), rewrite(((big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))), (((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(59,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) | (~big_p(a))) <=> ![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[58])).
% 0.40/0.59 tff(60,axiom,(![E: $i, F: $i] : ((((big_p(E) | big_p(F)) | big_p(sk1(F))) | big_r(sk4(E), sk3(E))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_3')).
% 0.40/0.59 tff(61,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.40/0.59 tff(62,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.40/0.59 tff(63,plain,(
% 0.40/0.59 ![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(skolemize,[status(sab)],[62])).
% 0.40/0.59 tff(64,plain,
% 0.40/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.40/0.59 tff(65,plain,
% 0.40/0.59 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(66,plain,
% 0.40/0.59 (((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(67,plain,
% 0.40/0.59 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[66])).
% 0.40/0.59 tff(68,plain,
% 0.40/0.59 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[67, 65])).
% 0.40/0.59 tff(69,plain,
% 0.40/0.59 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(70,plain,
% 0.40/0.59 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.40/0.59 tff(71,plain,
% 0.40/0.59 (big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[70, 64, 9, 5, 4])).
% 0.40/0.59 tff(72,plain,
% 0.40/0.59 (big_p(sk1(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[71, 54])).
% 0.40/0.59 tff(73,plain,
% 0.40/0.59 (^[L: $i, K: $i] : refl(((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(74,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[73])).
% 0.40/0.59 tff(75,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(76,plain,
% 0.40/0.59 (^[L: $i, K: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(K) | big_p(L)) | big_r(L, sk2(L))) <=> (big_p(L) | big_p(K) | big_r(L, sk2(L)))), ((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) <=> ((big_p(L) | big_p(K) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))))), rewrite(((big_p(L) | big_p(K) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) <=> (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))), ((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) <=> (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))))), (((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) | (~big_p(a))) <=> ((big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) | (~big_p(a))))), rewrite(((big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))), (((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(77,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) | (~big_p(a))) <=> ![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[76])).
% 0.40/0.59 tff(78,axiom,(![L: $i, K: $i] : ((((big_p(K) | big_p(L)) | big_r(L, sk2(L))) | big_r(sk4(K), sk3(K))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_6')).
% 0.40/0.59 tff(79,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.40/0.59 tff(80,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.40/0.59 tff(81,plain,(
% 0.40/0.59 ![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(skolemize,[status(sab)],[80])).
% 0.40/0.59 tff(82,plain,
% 0.40/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.40/0.59 tff(83,plain,
% 0.40/0.59 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(84,plain,
% 0.40/0.59 (((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(85,plain,
% 0.40/0.59 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[84])).
% 0.40/0.59 tff(86,plain,
% 0.40/0.59 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[85, 83])).
% 0.40/0.59 tff(87,plain,
% 0.40/0.59 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(88,plain,
% 0.40/0.59 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.40/0.59 tff(89,plain,
% 0.40/0.59 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[88, 82, 9, 5, 4])).
% 0.40/0.59 tff(90,plain,
% 0.40/0.59 (big_r(sk9, sk2(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[89, 54])).
% 0.40/0.59 tff(91,assumption,(~big_r(sk2(sk9), sk1(sk9))), introduced(assumption)).
% 0.40/0.59 tff(92,plain,
% 0.40/0.59 (^[E1: $i, F1: $i] : refl((big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1)) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1)))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(93,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1)) <=> ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[92])).
% 0.40/0.59 tff(94,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1)) <=> ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(95,plain,
% 0.40/0.59 (^[E1: $i, F1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_p(E1) | big_p(F1)) <=> (big_p(E1) | big_p(F1))), (((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) <=> ((big_p(E1) | big_p(F1)) | big_p(sk3(E1))))), rewrite(((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) <=> (big_p(sk3(E1)) | big_p(E1) | big_p(F1))), (((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) <=> (big_p(sk3(E1)) | big_p(E1) | big_p(F1)))), ((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) <=> ((big_p(sk3(E1)) | big_p(E1) | big_p(F1)) | big_r(sk2(F1), sk1(F1))))), rewrite(((big_p(sk3(E1)) | big_p(E1) | big_p(F1)) | big_r(sk2(F1), sk1(F1))) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))), ((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)))), (((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) | (~big_p(a))) <=> ((big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)) | (~big_p(a))))), rewrite(((big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)) | (~big_p(a))) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))), (((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) | (~big_p(a))) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(96,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : ((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) | (~big_p(a))) <=> ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[95])).
% 0.40/0.59 tff(97,axiom,(![E1: $i, F1: $i] : ((((big_p(E1) | big_p(F1)) | big_p(sk3(E1))) | big_r(sk2(F1), sk1(F1))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_13')).
% 0.40/0.59 tff(98,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.40/0.59 tff(99,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.40/0.59 tff(100,plain,(
% 0.40/0.59 ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(skolemize,[status(sab)],[99])).
% 0.40/0.59 tff(101,plain,
% 0.40/0.59 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.40/0.59 tff(102,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(103,plain,
% 0.40/0.59 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk9)) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(104,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[103])).
% 0.40/0.59 tff(105,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[104, 102])).
% 0.40/0.59 tff(106,plain,
% 0.40/0.59 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk9))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(107,plain,
% 0.40/0.59 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.40/0.59 tff(108,plain,
% 0.40/0.59 (big_p(sk3(sk7))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[107, 101, 9, 5, 4, 91])).
% 0.40/0.59 tff(109,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(110,plain,
% 0.40/0.59 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk9)) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(111,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[110])).
% 0.40/0.59 tff(112,plain,
% 0.40/0.59 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[111, 109])).
% 0.40/0.59 tff(113,plain,
% 0.40/0.59 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk9))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(114,plain,
% 0.40/0.59 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.40/0.59 tff(115,plain,
% 0.40/0.59 (big_p(sk3(sk9))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[114, 101, 9, 5, 91])).
% 0.40/0.59 tff(116,plain,
% 0.40/0.59 (^[H1: $i, G1: $i] : refl(((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(117,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[116])).
% 0.40/0.59 tff(118,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(119,plain,
% 0.40/0.59 (^[H1: $i, G1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) <=> (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)))), ((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) <=> ((big_p(H1) | big_p(G1) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))))), rewrite(((big_p(H1) | big_p(G1) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) <=> (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))), ((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) <=> (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))))), (((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) | (~big_p(a))) <=> ((big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) | (~big_p(a))))), rewrite(((big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))), (((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(120,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) | (~big_p(a))) <=> ![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[119])).
% 0.40/0.59 tff(121,axiom,(![H1: $i, G1: $i] : ((((big_p(G1) | big_p(H1)) | big_r(G1, sk4(G1))) | big_r(sk2(H1), sk1(H1))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_14')).
% 0.40/0.59 tff(122,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.40/0.59 tff(123,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.40/0.59 tff(124,plain,(
% 0.40/0.59 ![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(skolemize,[status(sab)],[123])).
% 0.40/0.59 tff(125,plain,
% 0.40/0.59 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.40/0.59 tff(126,plain,
% 0.40/0.59 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(127,plain,
% 0.40/0.59 (((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(128,plain,
% 0.40/0.59 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[127])).
% 0.40/0.60 tff(129,plain,
% 0.40/0.60 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[128, 126])).
% 0.40/0.60 tff(130,plain,
% 0.40/0.60 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(131,plain,
% 0.40/0.60 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.40/0.60 tff(132,plain,
% 0.40/0.60 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[131, 125, 9, 5])).
% 0.40/0.60 tff(133,plain,
% 0.40/0.60 (big_r(sk9, sk4(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[132, 91])).
% 0.40/0.60 tff(134,plain,
% 0.40/0.60 (^[J1: $i, I1: $i] : refl(((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))))),
% 0.40/0.60 inference(bind,[status(th)],[])).
% 0.40/0.60 tff(135,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(quant_intro,[status(thm)],[134])).
% 0.40/0.60 tff(136,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(137,plain,
% 0.40/0.60 (^[J1: $i, I1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) <=> (big_p(J1) | big_p(I1) | big_r(sk2(J1), sk1(J1)))), ((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) <=> ((big_p(J1) | big_p(I1) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))))), rewrite(((big_p(J1) | big_p(I1) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) <=> (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))), ((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) <=> (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))))), (((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) | (~big_p(a))) <=> ((big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) | (~big_p(a))))), rewrite(((big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))), (((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))))),
% 0.40/0.60 inference(bind,[status(th)],[])).
% 0.40/0.60 tff(138,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) | (~big_p(a))) <=> ![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(quant_intro,[status(thm)],[137])).
% 0.40/0.60 tff(139,axiom,(![J1: $i, I1: $i] : ((((big_p(I1) | big_p(J1)) | big_r(sk2(J1), sk1(J1))) | big_r(sk4(I1), sk3(I1))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_15')).
% 0.40/0.60 tff(140,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.40/0.60 tff(141,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.40/0.60 tff(142,plain,(
% 0.40/0.60 ![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(skolemize,[status(sab)],[141])).
% 0.40/0.60 tff(143,plain,
% 0.40/0.60 (![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.40/0.60 tff(144,plain,
% 0.40/0.60 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(145,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(146,plain,
% 0.40/0.60 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[145])).
% 0.40/0.60 tff(147,plain,
% 0.40/0.60 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[146, 144])).
% 0.40/0.60 tff(148,plain,
% 0.40/0.60 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(149,plain,
% 0.40/0.60 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.40/0.60 tff(150,plain,
% 0.40/0.60 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[149, 143, 9, 5])).
% 0.40/0.60 tff(151,plain,
% 0.40/0.60 (big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[150, 91])).
% 0.40/0.60 tff(152,assumption,(~big_r(sk7, sk4(sk7))), introduced(assumption)).
% 0.40/0.60 tff(153,plain,
% 0.40/0.60 (^[D: $i, C: $i] : refl(((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))))),
% 0.40/0.60 inference(bind,[status(th)],[])).
% 0.40/0.60 tff(154,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(quant_intro,[status(thm)],[153])).
% 0.40/0.60 tff(155,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(156,plain,
% 0.40/0.60 (^[D: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(C) | big_p(D)) | big_p(sk1(D))) <=> (big_p(sk1(D)) | big_p(D) | big_p(C))), ((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) <=> ((big_p(sk1(D)) | big_p(D) | big_p(C)) | big_r(C, sk4(C))))), rewrite(((big_p(sk1(D)) | big_p(D) | big_p(C)) | big_r(C, sk4(C))) <=> (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))), ((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) <=> (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))))), (((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) | (~big_p(a))) <=> ((big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) | (~big_p(a))))), rewrite(((big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))), (((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))))),
% 0.40/0.60 inference(bind,[status(th)],[])).
% 0.40/0.60 tff(157,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) | (~big_p(a))) <=> ![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(quant_intro,[status(thm)],[156])).
% 0.40/0.60 tff(158,axiom,(![D: $i, C: $i] : ((((big_p(C) | big_p(D)) | big_p(sk1(D))) | big_r(C, sk4(C))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_2')).
% 0.40/0.60 tff(159,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.40/0.60 tff(160,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.40/0.60 tff(161,plain,(
% 0.40/0.60 ![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(skolemize,[status(sab)],[160])).
% 0.40/0.60 tff(162,plain,
% 0.40/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.40/0.60 tff(163,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(164,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(165,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[164])).
% 0.40/0.60 tff(166,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[165, 163])).
% 0.40/0.60 tff(167,plain,
% 0.40/0.60 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(168,plain,
% 0.40/0.60 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.40/0.60 tff(169,plain,
% 0.40/0.60 (big_p(sk1(sk7))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[168, 162, 9, 4, 152])).
% 0.40/0.60 tff(170,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(171,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(172,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[171])).
% 0.40/0.60 tff(173,plain,
% 0.40/0.60 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[172, 170])).
% 0.40/0.60 tff(174,plain,
% 0.40/0.60 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(175,plain,
% 0.40/0.60 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.40/0.60 tff(176,plain,
% 0.40/0.60 (big_p(sk1(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[175, 162, 9, 5, 4, 152])).
% 0.40/0.60 tff(177,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(178,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(179,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[178])).
% 0.40/0.60 tff(180,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[179, 177])).
% 0.40/0.60 tff(181,plain,
% 0.40/0.60 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(182,plain,
% 0.40/0.60 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.40/0.60 tff(183,plain,
% 0.40/0.60 (big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[182, 45, 9, 5, 4])).
% 0.40/0.60 tff(184,plain,
% 0.40/0.60 (big_r(sk9, sk2(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[183, 152])).
% 0.40/0.60 tff(185,plain,
% 0.40/0.60 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(186,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(187,plain,
% 0.40/0.60 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[186])).
% 0.40/0.60 tff(188,plain,
% 0.40/0.60 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[187, 185])).
% 0.40/0.60 tff(189,plain,
% 0.40/0.60 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(190,plain,
% 0.40/0.60 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.40/0.60 tff(191,plain,
% 0.40/0.60 (big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[190, 125, 9, 5, 4])).
% 0.40/0.60 tff(192,plain,
% 0.40/0.60 (big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[191, 152])).
% 0.40/0.60 tff(193,assumption,(~big_r(sk7, sk2(sk7))), introduced(assumption)).
% 0.40/0.60 tff(194,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(195,plain,
% 0.40/0.60 (((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(196,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[195])).
% 0.40/0.60 tff(197,plain,
% 0.40/0.60 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[196, 194])).
% 0.40/0.61 tff(198,plain,
% 0.40/0.61 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(199,plain,
% 0.40/0.61 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.40/0.61 tff(200,plain,
% 0.40/0.61 (big_r(sk9, sk4(sk9))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[199, 45, 9, 5, 4, 193])).
% 0.40/0.61 tff(201,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(202,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(203,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[202])).
% 0.40/0.61 tff(204,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[203, 201])).
% 0.40/0.61 tff(205,plain,
% 0.40/0.61 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(206,plain,
% 0.40/0.61 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.40/0.61 tff(207,plain,
% 0.40/0.61 (big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[206, 82, 9, 5, 4, 193])).
% 0.40/0.61 tff(208,plain,
% 0.40/0.61 (^[H: $i, G: $i] : refl(((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(209,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[208])).
% 0.40/0.61 tff(210,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(211,plain,
% 0.40/0.61 (^[H: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(G) | big_p(H)) | big_p(sk3(G))) <=> (big_p(sk3(G)) | big_p(H) | big_p(G))), ((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) <=> ((big_p(sk3(G)) | big_p(H) | big_p(G)) | big_r(H, sk2(H))))), rewrite(((big_p(sk3(G)) | big_p(H) | big_p(G)) | big_r(H, sk2(H))) <=> (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))), ((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) <=> (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))))), (((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) | (~big_p(a))) <=> ((big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) | (~big_p(a))))), rewrite(((big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))), (((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(212,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) | (~big_p(a))) <=> ![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[211])).
% 0.40/0.61 tff(213,axiom,(![H: $i, G: $i] : ((((big_p(G) | big_p(H)) | big_p(sk3(G))) | big_r(H, sk2(H))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_4')).
% 0.40/0.61 tff(214,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.40/0.61 tff(215,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.40/0.61 tff(216,plain,(
% 0.40/0.61 ![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[215])).
% 0.40/0.61 tff(217,plain,
% 0.40/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.40/0.61 tff(218,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(219,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(220,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[219])).
% 0.40/0.61 tff(221,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[220, 218])).
% 0.40/0.61 tff(222,plain,
% 0.40/0.61 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(223,plain,
% 0.40/0.61 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.40/0.61 tff(224,plain,
% 0.40/0.61 (big_p(sk3(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[223, 217, 9, 4, 193])).
% 0.40/0.61 tff(225,plain,
% 0.40/0.61 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(226,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(227,plain,
% 0.40/0.61 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[226])).
% 0.40/0.61 tff(228,plain,
% 0.40/0.61 (((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[227, 225])).
% 0.40/0.61 tff(229,plain,
% 0.40/0.61 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(230,plain,
% 0.40/0.61 ((~![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.40/0.61 tff(231,plain,
% 0.40/0.61 (big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[230, 45, 9, 4])).
% 0.40/0.61 tff(232,plain,
% 0.40/0.61 (big_r(sk7, sk4(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[231, 193])).
% 0.40/0.61 tff(233,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(234,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(235,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[234])).
% 0.40/0.61 tff(236,plain,
% 0.40/0.61 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[235, 233])).
% 0.40/0.61 tff(237,plain,
% 0.40/0.61 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(238,plain,
% 0.40/0.61 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.40/0.61 tff(239,plain,
% 0.40/0.61 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[238, 82, 9, 4])).
% 0.40/0.61 tff(240,plain,
% 0.40/0.61 (big_r(sk4(sk7), sk3(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[239, 193])).
% 0.40/0.61 tff(241,plain,
% 0.40/0.61 (^[N4: $i, O4: $i, P4: $i, M4: $i] : refl(((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(242,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4))) <=> ![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[241])).
% 0.40/0.61 tff(243,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4))) <=> ![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(244,plain,
% 0.40/0.61 (^[N4: $i, O4: $i, P4: $i, M4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)))), (((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) <=> (((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4))) | (~big_r(P4, N4))))), rewrite((((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4))) | (~big_r(P4, N4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)))), (((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4))))), ((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) <=> (((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4))) | (~big_r(sk7, P4))))), rewrite((((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)))), ((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4))))), (((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) | (~big_r(sk9, O4))) <=> (((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4))) | (~big_r(sk9, O4))))), rewrite((((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4))) | (~big_r(sk9, O4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))), (((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) | (~big_r(sk9, O4))) <=> ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(245,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) | (~big_r(sk9, O4))) <=> ![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[244])).
% 0.40/0.61 tff(246,axiom,(![N4: $i, O4: $i, P4: $i, M4: $i] : ((((((~big_p(M4)) | (~big_p(N4))) | (~big_r(O4, M4))) | (~big_r(P4, N4))) | (~big_r(sk7, P4))) | (~big_r(sk9, O4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_46')).
% 0.40/0.61 tff(247,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.40/0.61 tff(248,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.40/0.61 tff(249,plain,(
% 0.40/0.61 ![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[248])).
% 0.40/0.61 tff(250,plain,
% 0.40/0.61 (![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.40/0.61 tff(251,plain,
% 0.40/0.61 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(252,plain,
% 0.40/0.61 (((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk4(sk9)))) <=> ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(253,plain,
% 0.40/0.61 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[252])).
% 0.40/0.61 tff(254,plain,
% 0.40/0.61 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.40/0.61 inference(transitivity,[status(thm)],[253, 251])).
% 0.40/0.61 tff(255,plain,
% 0.40/0.61 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk4(sk9))))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(256,plain,
% 0.40/0.61 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.40/0.61 tff(257,plain,
% 0.40/0.61 (~big_p(sk3(sk9))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[256, 250, 240, 232, 224, 207, 200])).
% 0.40/0.61 tff(258,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(259,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(260,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[259])).
% 0.40/0.61 tff(261,plain,
% 0.40/0.61 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[260, 258])).
% 0.40/0.61 tff(262,plain,
% 0.40/0.61 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(263,plain,
% 0.40/0.61 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.40/0.61 tff(264,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[263, 217, 9, 5, 4, 193, 257])).
% 0.40/0.61 tff(265,plain,(big_r(sk7, sk2(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(266,plain,
% 0.40/0.61 (big_r(sk7, sk2(sk7))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[265, 5, 4])).
% 0.40/0.61 tff(267,plain,
% 0.40/0.61 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(268,plain,
% 0.40/0.61 (((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(269,plain,
% 0.40/0.61 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[268])).
% 0.40/0.61 tff(270,plain,
% 0.40/0.61 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[269, 267])).
% 0.40/0.62 tff(271,plain,
% 0.40/0.62 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(272,plain,
% 0.40/0.62 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.40/0.62 tff(273,plain,
% 0.40/0.62 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[272, 125, 9, 4])).
% 0.40/0.62 tff(274,plain,
% 0.40/0.62 (big_r(sk2(sk7), sk1(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[273, 152])).
% 0.40/0.62 tff(275,plain,
% 0.40/0.62 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(276,plain,
% 0.40/0.62 (((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk2(sk9)))) <=> ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(277,plain,
% 0.40/0.62 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7)))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[276])).
% 0.40/0.62 tff(278,plain,
% 0.40/0.62 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[277, 275])).
% 0.40/0.62 tff(279,plain,
% 0.40/0.62 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk2(sk9))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(280,plain,
% 0.40/0.62 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))) | (~big_r(sk7, sk2(sk7)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.40/0.62 tff(281,plain,
% 0.40/0.62 ((~big_p(sk1(sk7))) | (~big_p(sk1(sk9)))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[280, 250, 274, 266, 192, 184])).
% 0.40/0.62 tff(282,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[281, 176, 169])).
% 0.40/0.62 tff(283,plain,(big_r(sk7, sk4(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(284,plain,
% 0.40/0.62 (big_r(sk7, sk4(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[283, 5, 4])).
% 0.40/0.62 tff(285,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(286,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(287,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[286])).
% 0.40/0.62 tff(288,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[287, 285])).
% 0.40/0.62 tff(289,plain,
% 0.40/0.62 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(290,plain,
% 0.40/0.62 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.40/0.62 tff(291,plain,
% 0.40/0.62 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[290, 143, 9, 5, 4])).
% 0.40/0.62 tff(292,plain,
% 0.40/0.62 (big_r(sk4(sk7), sk3(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[291, 91])).
% 0.40/0.62 tff(293,plain,
% 0.40/0.62 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[256, 250, 292, 284, 151, 133])).
% 0.40/0.62 tff(294,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[293, 115, 108])).
% 0.40/0.62 tff(295,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(296,plain,
% 0.40/0.62 (big_r(sk2(sk9), sk1(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[295, 5, 4])).
% 0.40/0.62 tff(297,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(298,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(299,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[298])).
% 0.40/0.62 tff(300,plain,
% 0.40/0.62 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[299, 297])).
% 0.40/0.62 tff(301,plain,
% 0.40/0.62 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(302,plain,
% 0.40/0.62 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.40/0.62 tff(303,plain,
% 0.40/0.62 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[302, 143, 9, 4])).
% 0.40/0.62 tff(304,plain,
% 0.40/0.62 (big_r(sk2(sk7), sk1(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[303, 54])).
% 0.40/0.62 tff(305,plain,
% 0.40/0.62 (~big_p(sk1(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[280, 250, 304, 266, 296, 90, 72])).
% 0.40/0.62 tff(306,plain,
% 0.40/0.62 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(307,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(308,plain,
% 0.40/0.62 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[307])).
% 0.40/0.62 tff(309,plain,
% 0.40/0.62 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[308, 306])).
% 0.40/0.62 tff(310,plain,
% 0.40/0.62 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(311,plain,
% 0.40/0.62 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.40/0.62 tff(312,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[311, 64, 9, 4, 54, 305])).
% 0.40/0.62 tff(313,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(314,plain,
% 0.40/0.62 (big_r(sk4(sk7), sk3(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[313, 5, 4])).
% 0.40/0.62 tff(315,plain,
% 0.40/0.62 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(316,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(317,plain,
% 0.40/0.62 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[316])).
% 0.40/0.62 tff(318,plain,
% 0.40/0.62 (((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[317, 315])).
% 0.40/0.62 tff(319,plain,
% 0.40/0.62 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(320,plain,
% 0.40/0.62 ((~![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.40/0.62 tff(321,plain,
% 0.40/0.62 (big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[320, 82, 9, 5])).
% 0.40/0.62 tff(322,plain,
% 0.40/0.62 (big_r(sk4(sk9), sk3(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[321, 3])).
% 0.40/0.62 tff(323,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(324,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(325,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[324])).
% 0.40/0.62 tff(326,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[325, 323])).
% 0.40/0.62 tff(327,plain,
% 0.40/0.62 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(328,plain,
% 0.40/0.62 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.40/0.62 tff(329,plain,
% 0.40/0.62 (big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[328, 217, 9, 5])).
% 0.40/0.62 tff(330,plain,
% 0.40/0.62 (big_p(sk3(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[329, 3])).
% 0.40/0.62 tff(331,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(332,plain,
% 0.40/0.62 (((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(333,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[332])).
% 0.40/0.62 tff(334,plain,
% 0.40/0.62 (((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[333, 331])).
% 0.40/0.62 tff(335,plain,
% 0.40/0.62 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | ((~big_p(a)) | big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(336,plain,
% 0.40/0.62 ((~![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.40/0.62 tff(337,plain,
% 0.40/0.62 (big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[336, 217, 9, 5, 4])).
% 0.40/0.62 tff(338,plain,
% 0.40/0.62 (big_p(sk3(sk7))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[337, 3])).
% 0.40/0.62 tff(339,assumption,(big_r(sk9, sk4(sk9))), introduced(assumption)).
% 0.40/0.62 tff(340,assumption,(big_r(sk4(sk9), sk3(sk9))), introduced(assumption)).
% 0.40/0.62 tff(341,assumption,(big_r(sk4(sk7), sk3(sk7))), introduced(assumption)).
% 0.40/0.62 tff(342,plain,
% 0.40/0.62 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[256, 250, 341, 284, 340, 339])).
% 0.40/0.62 tff(343,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[342, 338, 330])).
% 0.40/0.62 tff(344,plain,(big_r(sk9, sk2(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(345,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[344, 322, 3, 314, 53, 5, 4])).
% 0.40/0.62 tff(346,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(347,plain,
% 0.40/0.62 (big_r(sk9, sk2(sk9))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[346, 5, 4])).
% 0.40/0.62 tff(348,assumption,(~big_r(sk9, sk4(sk9))), introduced(assumption)).
% 0.40/0.62 tff(349,plain,
% 0.40/0.62 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(350,plain,
% 0.40/0.63 (((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(351,plain,
% 0.40/0.63 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))))),
% 0.40/0.63 inference(monotonicity,[status(thm)],[350])).
% 0.40/0.63 tff(352,plain,
% 0.40/0.63 (((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))) <=> ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.40/0.63 inference(transitivity,[status(thm)],[351, 349])).
% 0.40/0.63 tff(353,plain,
% 0.40/0.63 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | ((~big_p(a)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))),
% 0.40/0.63 inference(quant_inst,[status(thm)],[])).
% 0.40/0.63 tff(354,plain,
% 0.40/0.63 ((~![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | (~big_p(a)) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))),
% 0.40/0.63 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.40/0.63 tff(355,plain,
% 0.40/0.63 (big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[354, 162, 9, 5])).
% 0.40/0.63 tff(356,plain,
% 0.40/0.63 (big_p(sk1(sk9))),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[355, 348])).
% 0.40/0.63 tff(357,plain,
% 0.40/0.63 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(358,plain,
% 0.40/0.63 (((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk2(sk9)))) <=> ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(359,plain,
% 0.40/0.63 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))))),
% 0.40/0.63 inference(monotonicity,[status(thm)],[358])).
% 0.40/0.63 tff(360,plain,
% 0.40/0.63 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[359, 357])).
% 0.47/0.63 tff(361,plain,
% 0.47/0.63 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk2(sk9))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(362,plain,
% 0.47/0.63 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.47/0.63 tff(363,plain,
% 0.47/0.63 ((~big_p(sk3(sk7))) | (~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[362, 250, 314, 284, 296])).
% 0.47/0.63 tff(364,plain,
% 0.47/0.63 (~big_p(sk3(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[363, 356, 347])).
% 0.47/0.63 tff(365,plain,
% 0.47/0.63 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(366,plain,
% 0.47/0.63 (((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(367,plain,
% 0.47/0.63 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[366])).
% 0.47/0.63 tff(368,plain,
% 0.47/0.63 (((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[367, 365])).
% 0.47/0.63 tff(369,plain,
% 0.47/0.63 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(370,plain,
% 0.47/0.63 ((~![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.47/0.63 tff(371,plain,
% 0.47/0.63 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk4(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[370, 125, 9, 5, 4])).
% 0.47/0.63 tff(372,plain,
% 0.47/0.63 (big_r(sk2(sk7), sk1(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[371, 348])).
% 0.47/0.63 tff(373,plain,
% 0.47/0.63 (~big_p(sk1(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[280, 250, 372, 266, 296, 347, 356])).
% 0.47/0.63 tff(374,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[25, 19, 9, 4, 373, 364])).
% 0.47/0.63 tff(375,plain,(big_r(sk9, sk4(sk9)) | big_p(sk7) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(376,plain,
% 0.47/0.63 (big_r(sk9, sk4(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[375, 5, 4])).
% 0.47/0.63 tff(377,assumption,(~big_r(sk4(sk9), sk3(sk9))), introduced(assumption)).
% 0.47/0.63 tff(378,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(379,plain,
% 0.47/0.63 (((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(380,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[379])).
% 0.47/0.63 tff(381,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[380, 378])).
% 0.47/0.63 tff(382,plain,
% 0.47/0.63 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(383,plain,
% 0.47/0.63 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.47/0.63 tff(384,plain,
% 0.47/0.63 (big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[383, 64, 9, 5])).
% 0.47/0.63 tff(385,plain,
% 0.47/0.63 (big_p(sk1(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[384, 377])).
% 0.47/0.63 tff(386,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(387,plain,
% 0.47/0.63 (((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(388,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[387])).
% 0.47/0.63 tff(389,plain,
% 0.47/0.63 (((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[388, 386])).
% 0.47/0.63 tff(390,plain,
% 0.47/0.63 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | ((~big_p(a)) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(391,plain,
% 0.47/0.63 ((~![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.47/0.63 tff(392,plain,
% 0.47/0.63 (big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[391, 64, 9, 5, 4])).
% 0.47/0.63 tff(393,plain,
% 0.47/0.63 (big_p(sk1(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[392, 377])).
% 0.47/0.63 tff(394,assumption,(~big_r(sk2(sk7), sk1(sk7))), introduced(assumption)).
% 0.47/0.63 tff(395,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(396,plain,
% 0.47/0.63 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk7)) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(397,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[396])).
% 0.47/0.63 tff(398,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[397, 395])).
% 0.47/0.63 tff(399,plain,
% 0.47/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | big_p(sk7))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(400,plain,
% 0.47/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.47/0.63 tff(401,plain,
% 0.47/0.63 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[400, 101, 9, 4])).
% 0.47/0.63 tff(402,plain,
% 0.47/0.63 (big_p(sk3(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[401, 394])).
% 0.47/0.63 tff(403,plain,
% 0.47/0.63 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(404,plain,
% 0.47/0.63 (((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(405,plain,
% 0.47/0.63 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[404])).
% 0.47/0.63 tff(406,plain,
% 0.47/0.63 (((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[405, 403])).
% 0.47/0.63 tff(407,plain,
% 0.47/0.63 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(408,plain,
% 0.47/0.63 ((~![J1: $i, I1: $i] : ((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.47/0.63 tff(409,plain,
% 0.47/0.63 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[408, 143, 9, 5, 4])).
% 0.47/0.63 tff(410,plain,
% 0.47/0.63 (big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[409, 394])).
% 0.47/0.63 tff(411,plain,
% 0.47/0.63 (~big_p(sk3(sk9))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[256, 250, 314, 284, 410, 376, 402])).
% 0.47/0.63 tff(412,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(413,plain,
% 0.47/0.63 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk7)) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(414,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[413])).
% 0.47/0.63 tff(415,plain,
% 0.47/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[414, 412])).
% 0.47/0.63 tff(416,plain,
% 0.47/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | big_p(sk7))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(417,plain,
% 0.47/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))) | big_p(sk9) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.47/0.63 tff(418,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[417, 101, 9, 5, 4, 394, 411])).
% 0.47/0.63 tff(419,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(420,plain,
% 0.47/0.63 (big_r(sk2(sk7), sk1(sk7))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[419, 5, 4])).
% 0.47/0.63 tff(421,plain,
% 0.47/0.63 ((~big_p(sk1(sk7))) | (~big_p(sk1(sk9)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[280, 250, 420, 266, 296, 347])).
% 0.47/0.63 tff(422,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[421, 393, 385])).
% 0.47/0.64 tff(423,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(424,plain,
% 0.47/0.64 (big_r(sk4(sk9), sk3(sk9))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[423, 5, 4])).
% 0.47/0.64 tff(425,plain,
% 0.47/0.64 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[256, 250, 314, 284, 424, 376])).
% 0.47/0.64 tff(426,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[425, 35, 27])).
% 0.47/0.64 tff(427,plain,(big_p(sk1(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(428,plain,
% 0.47/0.64 (big_p(sk1(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[427, 5, 4])).
% 0.47/0.64 tff(429,plain,
% 0.47/0.64 (~big_p(sk1(sk9))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[421, 428])).
% 0.47/0.64 tff(430,plain,
% 0.47/0.64 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(431,plain,
% 0.47/0.64 (((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk4(sk9)))) <=> ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(432,plain,
% 0.47/0.64 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[431])).
% 0.47/0.64 tff(433,plain,
% 0.47/0.64 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[432, 430])).
% 0.47/0.64 tff(434,plain,
% 0.47/0.64 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk4(sk9))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(435,plain,
% 0.47/0.64 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk2(sk7)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.47/0.64 tff(436,plain,
% 0.47/0.64 ((~big_p(sk1(sk7))) | (~big_p(sk3(sk9)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[435, 250, 420, 266, 424, 376])).
% 0.47/0.64 tff(437,plain,
% 0.47/0.64 (~big_p(sk3(sk9))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[436, 428])).
% 0.47/0.64 tff(438,plain,
% 0.47/0.64 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(439,plain,
% 0.47/0.64 (((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9)) <=> (big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(440,plain,
% 0.47/0.64 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[439])).
% 0.47/0.64 tff(441,plain,
% 0.47/0.64 (((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[440, 438])).
% 0.47/0.64 tff(442,plain,
% 0.47/0.64 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(443,plain,
% 0.47/0.64 ((~![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | (~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk9))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.47/0.64 tff(444,plain,
% 0.47/0.64 (big_p(sk3(sk9)) | big_p(sk1(sk9))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[443, 19, 9, 5])).
% 0.47/0.64 tff(445,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[444, 437, 429])).
% 0.47/0.64 tff(446,plain,(big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(447,plain,
% 0.47/0.64 (big_p(sk9)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[446, 4])).
% 0.47/0.64 tff(448,assumption,(~big_r(sk9, sk10)), introduced(assumption)).
% 0.47/0.64 tff(449,plain,
% 0.47/0.64 (big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[223, 217, 9, 4])).
% 0.47/0.64 tff(450,plain,
% 0.47/0.64 (big_p(sk3(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[449, 193])).
% 0.47/0.64 tff(451,plain,
% 0.47/0.64 (big_r(sk7, sk2(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[239, 54])).
% 0.47/0.64 tff(452,plain,
% 0.47/0.64 (^[L4: $i, K4: $i] : refl(((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4))) <=> ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(453,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4))) <=> ![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[452])).
% 0.47/0.64 tff(454,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4))) <=> ![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(455,plain,
% 0.47/0.64 (^[L4: $i, K4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_r(sk9, sk10) | (~big_p(K4))) <=> ((~big_p(K4)) | big_r(sk9, sk10))), (((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) <=> (((~big_p(K4)) | big_r(sk9, sk10)) | (~big_p(sk9))))), rewrite((((~big_p(K4)) | big_r(sk9, sk10)) | (~big_p(sk9))) <=> ((~big_p(sk9)) | (~big_p(K4)) | big_r(sk9, sk10))), (((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) <=> ((~big_p(sk9)) | (~big_p(K4)) | big_r(sk9, sk10)))), ((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) <=> (((~big_p(sk9)) | (~big_p(K4)) | big_r(sk9, sk10)) | (~big_r(L4, K4))))), rewrite((((~big_p(sk9)) | (~big_p(K4)) | big_r(sk9, sk10)) | (~big_r(L4, K4))) <=> ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10))), ((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) <=> ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10)))), (((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) | (~big_r(sk7, L4))) <=> (((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10)) | (~big_r(sk7, L4))))), rewrite((((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10)) | (~big_r(sk7, L4))) <=> ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))), (((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) | (~big_r(sk7, L4))) <=> ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(456,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) | (~big_r(sk7, L4))) <=> ![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[455])).
% 0.47/0.64 tff(457,axiom,(![L4: $i, K4: $i] : ((((big_r(sk9, sk10) | (~big_p(K4))) | (~big_p(sk9))) | (~big_r(L4, K4))) | (~big_r(sk7, L4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_45')).
% 0.47/0.64 tff(458,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.47/0.64 tff(459,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[458, 454])).
% 0.47/0.64 tff(460,plain,(
% 0.47/0.64 ![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[459])).
% 0.47/0.64 tff(461,plain,
% 0.47/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[460, 453])).
% 0.47/0.64 tff(462,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(463,plain,
% 0.47/0.64 (((~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk2(sk7)))) <=> ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(464,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk2(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[463])).
% 0.47/0.64 tff(465,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk2(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[464, 462])).
% 0.47/0.64 tff(466,plain,
% 0.47/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(467,plain,
% 0.47/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.47/0.64 tff(468,plain,
% 0.47/0.64 (~big_p(sk1(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[467, 447, 448, 461, 304, 451])).
% 0.47/0.64 tff(469,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[311, 64, 9, 4, 54, 468])).
% 0.47/0.64 tff(470,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(471,plain,
% 0.47/0.64 (big_r(sk4(sk7), sk3(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[470, 4, 448])).
% 0.47/0.64 tff(472,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(473,plain,
% 0.47/0.64 (((~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk4(sk7)))) <=> ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(474,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk4(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[473])).
% 0.47/0.64 tff(475,plain,
% 0.47/0.64 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk4(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[474, 472])).
% 0.47/0.64 tff(476,plain,
% 0.47/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(477,plain,
% 0.47/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.47/0.64 tff(478,plain,
% 0.47/0.64 ((~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[477, 447, 448, 461, 471])).
% 0.47/0.64 tff(479,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[478, 450, 232])).
% 0.47/0.64 tff(480,plain,(big_r(sk7, sk2(sk7)) | big_r(sk9, sk10) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(481,plain,
% 0.47/0.64 (big_r(sk7, sk2(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[480, 4, 448])).
% 0.47/0.64 tff(482,plain,
% 0.47/0.64 (~big_p(sk1(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[467, 447, 448, 461, 274, 481])).
% 0.47/0.64 tff(483,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[168, 162, 9, 4, 152, 482])).
% 0.47/0.64 tff(484,plain,(big_r(sk7, sk4(sk7)) | big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(485,plain,
% 0.47/0.64 (big_r(sk7, sk4(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[484, 4, 448])).
% 0.47/0.64 tff(486,plain,
% 0.47/0.64 (~big_p(sk3(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[478, 485])).
% 0.47/0.64 tff(487,plain,
% 0.47/0.64 (big_r(sk2(sk7), sk1(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[401, 486])).
% 0.47/0.64 tff(488,plain,
% 0.47/0.64 (~big_p(sk1(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[467, 447, 448, 461, 487, 481])).
% 0.47/0.64 tff(489,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[25, 19, 9, 4, 488, 486])).
% 0.47/0.64 tff(490,plain,(big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(491,plain,
% 0.47/0.64 (big_r(sk9, sk10)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[490, 4])).
% 0.47/0.64 tff(492,assumption,(big_p(sk9)), introduced(assumption)).
% 0.47/0.64 tff(493,assumption,(~big_p(sk10)), introduced(assumption)).
% 0.47/0.64 tff(494,plain,
% 0.47/0.64 (big_r(sk7, sk4(sk7))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[273, 394])).
% 0.47/0.64 tff(495,plain,
% 0.47/0.64 (^[J4: $i, I4: $i] : refl((big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(496,plain,
% 0.47/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4))) <=> ![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[495])).
% 0.47/0.64 tff(497,plain,
% 0.47/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4))) <=> ![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(498,plain,
% 0.47/0.64 (^[J4: $i, I4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_p(I4)))), ((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) <=> ((big_p(sk10) | (~big_p(sk9)) | (~big_p(I4))) | (~big_r(J4, I4))))), rewrite(((big_p(sk10) | (~big_p(sk9)) | (~big_p(I4))) | (~big_r(J4, I4))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)))), ((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4))))), (((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) | (~big_r(sk7, J4))) <=> ((big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4))) | (~big_r(sk7, J4))))), rewrite(((big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4))) | (~big_r(sk7, J4))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))), (((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) | (~big_r(sk7, J4))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(499,plain,
% 0.47/0.64 (![J4: $i, I4: $i] : ((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) | (~big_r(sk7, J4))) <=> ![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[498])).
% 0.47/0.64 tff(500,axiom,(![J4: $i, I4: $i] : ((((big_p(sk10) | (~big_p(I4))) | (~big_p(sk9))) | (~big_r(J4, I4))) | (~big_r(sk7, J4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_44')).
% 0.47/0.64 tff(501,plain,
% 0.47/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.47/0.64 tff(502,plain,
% 0.47/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[501, 497])).
% 0.47/0.65 tff(503,plain,(
% 0.47/0.65 ![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[502])).
% 0.47/0.65 tff(504,plain,
% 0.47/0.65 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[503, 496])).
% 0.47/0.65 tff(505,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(506,plain,
% 0.47/0.65 ((big_p(sk10) | (~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7)))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(507,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[506])).
% 0.47/0.65 tff(508,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[507, 505])).
% 0.47/0.65 tff(509,plain,
% 0.47/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(510,plain,
% 0.47/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.47/0.65 tff(511,plain,
% 0.47/0.65 (~big_p(sk3(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[510, 493, 492, 504, 232, 240])).
% 0.47/0.65 tff(512,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[223, 217, 9, 4, 193, 511])).
% 0.47/0.65 tff(513,plain,(big_r(sk7, sk2(sk7)) | big_p(sk7) | big_p(sk10) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(514,plain,
% 0.47/0.65 (big_r(sk7, sk2(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[513, 493, 4, 492])).
% 0.47/0.65 tff(515,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(516,plain,
% 0.47/0.65 ((big_p(sk10) | (~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7)))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(517,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[516])).
% 0.47/0.65 tff(518,plain,
% 0.47/0.65 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[517, 515])).
% 0.47/0.65 tff(519,plain,
% 0.47/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(520,plain,
% 0.47/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.47/0.65 tff(521,plain,
% 0.47/0.65 (~big_p(sk1(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[520, 493, 492, 504, 514, 304])).
% 0.47/0.65 tff(522,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[311, 64, 9, 4, 54, 521])).
% 0.47/0.65 tff(523,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_p(sk10) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(524,plain,
% 0.47/0.65 (big_r(sk4(sk7), sk3(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[523, 493, 4, 492])).
% 0.47/0.65 tff(525,plain,
% 0.47/0.65 ((~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[510, 493, 492, 504, 524])).
% 0.47/0.65 tff(526,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[525, 402, 494])).
% 0.47/0.65 tff(527,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk10) | (~big_p(sk9)) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(528,plain,
% 0.47/0.65 (big_r(sk2(sk7), sk1(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[527, 493, 492, 4])).
% 0.47/0.65 tff(529,plain,
% 0.47/0.65 (~big_p(sk1(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[520, 493, 492, 504, 514, 528])).
% 0.47/0.65 tff(530,plain,
% 0.47/0.65 (big_p(sk3(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[25, 19, 9, 4, 529])).
% 0.47/0.65 tff(531,plain,
% 0.47/0.65 (big_r(sk7, sk4(sk7))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[168, 162, 9, 4, 529])).
% 0.47/0.65 tff(532,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[525, 531, 530])).
% 0.47/0.65 tff(533,plain,(big_p(sk10) | (~big_p(sk9)) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(534,plain,
% 0.47/0.65 (big_p(sk10)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[533, 4, 492])).
% 0.47/0.65 tff(535,assumption,(big_r(sk9, sk10)), introduced(assumption)).
% 0.47/0.65 tff(536,assumption,(big_p(sk10)), introduced(assumption)).
% 0.47/0.65 tff(537,plain,
% 0.47/0.65 (^[O: $i, N: $i, M: $i] : refl(((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))) <=> ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(538,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))) <=> ![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[537])).
% 0.47/0.65 tff(539,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))) <=> ![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(540,plain,
% 0.47/0.65 (^[O: $i, N: $i, M: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) <=> (big_p(M) | big_p(sk1(M)) | big_p(sk5(N)))), ((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) <=> ((big_p(M) | big_p(sk1(M)) | big_p(sk5(N))) | (~big_p(O))))), rewrite(((big_p(M) | big_p(sk1(M)) | big_p(sk5(N))) | (~big_p(O))) <=> (big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N)))), ((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) <=> (big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))))), (((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) <=> ((big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))) | (~big_p(a))))), rewrite(((big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N)))), (((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))))), ((((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) | (~big_r(N, O))) <=> (((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))) | (~big_r(N, O))))), rewrite((((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_p(O)) | big_p(sk5(N))) | (~big_r(N, O))) <=> ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))), ((((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) | (~big_r(N, O))) <=> ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(541,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : (((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) | (~big_r(N, O))) <=> ![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[540])).
% 0.47/0.65 tff(542,axiom,(![O: $i, N: $i, M: $i] : (((((big_p(M) | big_p(sk1(M))) | big_p(sk5(N))) | (~big_p(O))) | (~big_p(a))) | (~big_r(N, O)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_7')).
% 0.47/0.65 tff(543,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.47/0.65 tff(544,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[543, 539])).
% 0.47/0.65 tff(545,plain,(
% 0.47/0.65 ![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[544])).
% 0.47/0.65 tff(546,plain,
% 0.47/0.65 (![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[545, 538])).
% 0.47/0.65 tff(547,plain,
% 0.47/0.65 (((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))) <=> ((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(548,plain,
% 0.47/0.65 (((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9))) <=> ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(549,plain,
% 0.47/0.65 (((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9)))) <=> ((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[548])).
% 0.47/0.65 tff(550,plain,
% 0.47/0.65 (((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9)))) <=> ((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[549, 547])).
% 0.47/0.65 tff(551,plain,
% 0.47/0.65 ((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(552,plain,
% 0.47/0.65 ((~![O: $i, N: $i, M: $i] : ((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.47/0.65 tff(553,plain,
% 0.47/0.65 (big_p(sk1(sk7)) | big_p(sk5(sk9))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[552, 546, 9, 536, 4, 535])).
% 0.47/0.65 tff(554,plain,
% 0.47/0.65 (big_p(sk5(sk9))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[553, 6])).
% 0.47/0.65 tff(555,plain,
% 0.47/0.65 (^[R: $i, Q: $i, P: $i] : refl(((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))) <=> ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(556,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))) <=> ![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[555])).
% 0.47/0.65 tff(557,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))) <=> ![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(558,plain,
% 0.47/0.65 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) <=> (big_p(P) | big_p(sk1(P)) | big_r(Q, sk6(Q)))), ((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) <=> ((big_p(P) | big_p(sk1(P)) | big_r(Q, sk6(Q))) | (~big_p(R))))), rewrite(((big_p(P) | big_p(sk1(P)) | big_r(Q, sk6(Q))) | (~big_p(R))) <=> (big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q)))), ((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) <=> (big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))))), (((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) <=> ((big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))) | (~big_p(a))))), rewrite(((big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q)))), (((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))))), ((((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) | (~big_r(Q, R))) <=> (((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))) | (~big_r(Q, R))))), rewrite((((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_p(R)) | big_r(Q, sk6(Q))) | (~big_r(Q, R))) <=> ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))), ((((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) | (~big_r(Q, R))) <=> ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(559,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : (((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) | (~big_r(Q, R))) <=> ![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[558])).
% 0.47/0.65 tff(560,axiom,(![R: $i, Q: $i, P: $i] : (((((big_p(P) | big_p(sk1(P))) | big_r(Q, sk6(Q))) | (~big_p(R))) | (~big_p(a))) | (~big_r(Q, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_8')).
% 0.47/0.65 tff(561,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.47/0.65 tff(562,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[561, 557])).
% 0.47/0.65 tff(563,plain,(
% 0.47/0.65 ![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[562])).
% 0.47/0.65 tff(564,plain,
% 0.47/0.65 (![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[563, 556])).
% 0.47/0.65 tff(565,plain,
% 0.47/0.65 (((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(566,plain,
% 0.47/0.65 (((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))) <=> ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(567,plain,
% 0.47/0.65 (((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[566])).
% 0.47/0.65 tff(568,plain,
% 0.47/0.65 (((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[567, 565])).
% 0.47/0.65 tff(569,plain,
% 0.47/0.65 ((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(570,plain,
% 0.47/0.65 ((~![R: $i, Q: $i, P: $i] : ((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.47/0.65 tff(571,plain,
% 0.47/0.65 (big_p(sk1(sk7)) | big_r(sk9, sk6(sk9))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[570, 564, 9, 536, 4, 535])).
% 0.47/0.65 tff(572,plain,
% 0.47/0.65 (big_r(sk9, sk6(sk9))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[571, 6])).
% 0.47/0.65 tff(573,plain,
% 0.47/0.65 (^[S: $i, T: $i, U: $i] : refl(((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(574,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> ![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[573])).
% 0.47/0.65 tff(575,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> ![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(576,plain,
% 0.47/0.65 (^[S: $i, T: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) <=> (big_p(S) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))), ((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) <=> ((big_p(S) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_p(U))))), rewrite(((big_p(S) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_p(U))) <=> (big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))), ((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) <=> (big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))))), (((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) <=> ((big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_p(a))))), rewrite(((big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))), (((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))))), ((((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) | (~big_r(T, U))) <=> (((~big_p(a)) | big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_r(T, U))))), rewrite((((~big_p(a)) | big_p(S) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) | (~big_r(T, U))) <=> ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))), ((((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) | (~big_r(T, U))) <=> ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(577,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : (((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) | (~big_r(T, U))) <=> ![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[576])).
% 0.47/0.65 tff(578,axiom,(![S: $i, T: $i, U: $i] : (((((big_p(S) | big_p(sk1(S))) | big_r(sk6(T), sk5(T))) | (~big_p(U))) | (~big_p(a))) | (~big_r(T, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_9')).
% 0.47/0.65 tff(579,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.47/0.65 tff(580,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[579, 575])).
% 0.47/0.65 tff(581,plain,(
% 0.47/0.65 ![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[580])).
% 0.47/0.65 tff(582,plain,
% 0.47/0.65 (![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[581, 574])).
% 0.47/0.65 tff(583,plain,
% 0.47/0.65 (((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(584,plain,
% 0.47/0.66 (((~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(585,plain,
% 0.47/0.66 (((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | ((~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7)))) <=> ((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[584])).
% 0.47/0.66 tff(586,plain,
% 0.47/0.66 (((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | ((~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7)))) <=> ((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[585, 583])).
% 0.47/0.66 tff(587,plain,
% 0.47/0.66 ((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | ((~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(588,plain,
% 0.47/0.66 ((~![S: $i, T: $i, U: $i] : ((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.47/0.66 tff(589,plain,
% 0.47/0.66 (big_p(sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[588, 582, 9, 536, 4, 535])).
% 0.47/0.66 tff(590,plain,
% 0.47/0.66 (big_r(sk6(sk9), sk5(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[589, 6])).
% 0.47/0.66 tff(591,plain,
% 0.47/0.66 (^[D2: $i, E2: $i, C2: $i] : refl(((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(592,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> ![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[591])).
% 0.47/0.66 tff(593,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> ![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(594,plain,
% 0.47/0.66 (^[D2: $i, E2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) <=> (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)))), ((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) <=> ((big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2))) | (~big_p(E2))))), rewrite(((big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2))) | (~big_p(E2))) <=> (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2)))), ((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) <=> (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))))), (((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) <=> ((big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))) | (~big_p(a))))), rewrite(((big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2)))), (((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))))), ((((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) | (~big_r(D2, E2))) <=> (((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))) | (~big_r(D2, E2))))), rewrite((((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_p(E2))) | (~big_r(D2, E2))) <=> ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))), ((((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) | (~big_r(D2, E2))) <=> ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(595,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : (((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) | (~big_r(D2, E2))) <=> ![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[594])).
% 0.47/0.66 tff(596,axiom,(![D2: $i, E2: $i, C2: $i] : (((((big_p(C2) | big_p(sk1(D2))) | big_r(sk4(C2), sk3(C2))) | (~big_p(E2))) | (~big_p(a))) | (~big_r(D2, E2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_22')).
% 0.47/0.66 tff(597,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.47/0.66 tff(598,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[597, 593])).
% 0.47/0.66 tff(599,plain,(
% 0.47/0.66 ![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[598])).
% 0.47/0.66 tff(600,plain,
% 0.47/0.66 (![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[599, 592])).
% 0.47/0.66 tff(601,plain,
% 0.47/0.66 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(602,plain,
% 0.47/0.66 (((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(603,plain,
% 0.47/0.66 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[602])).
% 0.47/0.66 tff(604,plain,
% 0.47/0.66 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[603, 601])).
% 0.47/0.66 tff(605,plain,
% 0.47/0.66 ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(606,plain,
% 0.47/0.66 ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.47/0.66 tff(607,plain,
% 0.47/0.66 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_p(sk1(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[606, 600, 9, 4, 535])).
% 0.47/0.66 tff(608,plain,
% 0.47/0.66 (big_p(sk1(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[607, 54, 536])).
% 0.47/0.66 tff(609,plain,
% 0.47/0.66 (^[K2: $i, I2: $i, J2: $i] : refl((big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))) <=> (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(610,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))) <=> ![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[609])).
% 0.47/0.66 tff(611,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))) <=> ![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(612,plain,
% 0.47/0.66 (^[K2: $i, I2: $i, J2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) <=> (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)))), ((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) <=> ((big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))))), rewrite(((big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) <=> (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)))), ((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) <=> (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))))), (((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) <=> ((big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))) | (~big_p(a))))), rewrite(((big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))) | (~big_p(a))) <=> (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)))), (((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) <=> (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))))), ((((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) | (~big_r(J2, K2))) <=> ((big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))) | (~big_r(J2, K2))))), rewrite(((big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2))) | (~big_r(J2, K2))) <=> (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))), ((((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) | (~big_r(J2, K2))) <=> (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(613,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) | (~big_r(J2, K2))) <=> ![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[612])).
% 0.47/0.66 tff(614,axiom,(![K2: $i, I2: $i, J2: $i] : (((((big_p(I2) | big_r(sk2(J2), sk1(J2))) | big_r(sk4(I2), sk3(I2))) | (~big_p(K2))) | (~big_p(a))) | (~big_r(J2, K2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_24')).
% 0.47/0.66 tff(615,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.47/0.66 tff(616,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.47/0.66 tff(617,plain,(
% 0.47/0.66 ![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[616])).
% 0.47/0.66 tff(618,plain,
% 0.47/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.47/0.66 tff(619,plain,
% 0.47/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(620,plain,
% 0.47/0.66 ((big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(621,plain,
% 0.47/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[620])).
% 0.47/0.66 tff(622,plain,
% 0.47/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[621, 619])).
% 0.47/0.66 tff(623,plain,
% 0.47/0.66 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(624,plain,
% 0.47/0.66 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.47/0.66 tff(625,plain,
% 0.47/0.66 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[624, 618, 9, 4, 535])).
% 0.47/0.66 tff(626,plain,
% 0.47/0.66 (big_r(sk2(sk9), sk1(sk9))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[625, 54, 536])).
% 0.47/0.66 tff(627,plain,
% 0.47/0.66 (^[G2: $i, H2: $i, F2: $i] : refl(((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) <=> ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(628,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) <=> ![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[627])).
% 0.47/0.66 tff(629,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) <=> ![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(630,plain,
% 0.47/0.66 (^[G2: $i, H2: $i, F2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) <=> (big_p(F2) | big_r(sk4(F2), sk3(F2)) | big_r(G2, sk2(G2)))), ((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) <=> ((big_p(F2) | big_r(sk4(F2), sk3(F2)) | big_r(G2, sk2(G2))) | (~big_p(H2))))), rewrite(((big_p(F2) | big_r(sk4(F2), sk3(F2)) | big_r(G2, sk2(G2))) | (~big_p(H2))) <=> (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))), ((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) <=> (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))))), (((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) <=> ((big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) | (~big_p(a))))), rewrite(((big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))), (((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))))), ((((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) | (~big_r(G2, H2))) <=> (((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) | (~big_r(G2, H2))))), rewrite((((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) | (~big_r(G2, H2))) <=> ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))), ((((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) | (~big_r(G2, H2))) <=> ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(631,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : (((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) | (~big_r(G2, H2))) <=> ![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[630])).
% 0.47/0.66 tff(632,axiom,(![G2: $i, H2: $i, F2: $i] : (((((big_p(F2) | big_r(G2, sk2(G2))) | big_r(sk4(F2), sk3(F2))) | (~big_p(H2))) | (~big_p(a))) | (~big_r(G2, H2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_23')).
% 0.47/0.66 tff(633,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.47/0.66 tff(634,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[633, 629])).
% 0.47/0.66 tff(635,plain,(
% 0.47/0.66 ![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[634])).
% 0.47/0.66 tff(636,plain,
% 0.47/0.66 (![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[635, 628])).
% 0.47/0.66 tff(637,plain,
% 0.47/0.66 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(638,plain,
% 0.47/0.66 (((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(639,plain,
% 0.47/0.66 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[638])).
% 0.47/0.66 tff(640,plain,
% 0.47/0.66 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[639, 637])).
% 0.47/0.66 tff(641,plain,
% 0.47/0.66 ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(642,plain,
% 0.47/0.66 ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.47/0.67 tff(643,plain,
% 0.47/0.67 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[642, 636, 9, 4, 535])).
% 0.47/0.67 tff(644,plain,
% 0.47/0.67 (big_r(sk9, sk2(sk9))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[643, 54, 536])).
% 0.47/0.67 tff(645,plain,
% 0.47/0.67 (~big_p(sk1(sk7))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[280, 250, 451, 304, 644, 626, 608])).
% 0.47/0.67 tff(646,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[311, 64, 9, 4, 54, 645])).
% 0.47/0.67 tff(647,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.67 tff(648,plain,
% 0.47/0.67 (big_r(sk4(sk7), sk3(sk7))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[647, 4, 536, 535])).
% 0.47/0.67 tff(649,plain,
% 0.47/0.67 (^[R1: $i, S1: $i, Q1: $i] : refl(((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(650,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> ![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[649])).
% 0.50/0.67 tff(651,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> ![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(652,plain,
% 0.50/0.67 (^[R1: $i, S1: $i, Q1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) <=> (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)))), ((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) <=> ((big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1))) | (~big_p(S1))))), rewrite(((big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1))) | (~big_p(S1))) <=> (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1)))), ((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) <=> (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))))), (((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) <=> ((big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))) | (~big_p(a))))), rewrite(((big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1)))), (((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))))), ((((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) | (~big_r(R1, S1))) <=> (((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))) | (~big_r(R1, S1))))), rewrite((((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_p(S1))) | (~big_r(R1, S1))) <=> ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))), ((((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) | (~big_r(R1, S1))) <=> ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(653,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : (((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) | (~big_r(R1, S1))) <=> ![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[652])).
% 0.50/0.67 tff(654,axiom,(![R1: $i, S1: $i, Q1: $i] : (((((big_p(Q1) | big_p(sk1(R1))) | big_r(Q1, sk4(Q1))) | (~big_p(S1))) | (~big_p(a))) | (~big_r(R1, S1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_18')).
% 0.50/0.67 tff(655,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.50/0.67 tff(656,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[655, 651])).
% 0.50/0.67 tff(657,plain,(
% 0.50/0.67 ![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[656])).
% 0.50/0.67 tff(658,plain,
% 0.50/0.67 (![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[657, 650])).
% 0.50/0.67 tff(659,plain,
% 0.50/0.67 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(660,plain,
% 0.50/0.67 (((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(661,plain,
% 0.50/0.67 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[660])).
% 0.50/0.67 tff(662,plain,
% 0.50/0.67 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[661, 659])).
% 0.50/0.67 tff(663,plain,
% 0.50/0.67 ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(664,plain,
% 0.50/0.67 ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.50/0.67 tff(665,plain,
% 0.50/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_p(sk1(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[664, 658, 9, 4, 535])).
% 0.50/0.67 tff(666,plain,
% 0.50/0.67 (big_p(sk1(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[665, 152, 536])).
% 0.50/0.67 tff(667,plain,
% 0.50/0.67 (big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[168, 162, 9, 4])).
% 0.50/0.67 tff(668,plain,
% 0.50/0.67 (big_p(sk1(sk7))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[667, 152])).
% 0.50/0.67 tff(669,plain,
% 0.50/0.67 (^[A2: $i, B2: $i, Z1: $i] : refl(((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) <=> ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(670,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) <=> ![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[669])).
% 0.50/0.67 tff(671,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) <=> ![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(672,plain,
% 0.50/0.67 (^[A2: $i, B2: $i, Z1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) <=> (big_p(Z1) | big_r(Z1, sk4(Z1)) | big_r(sk2(A2), sk1(A2)))), ((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) <=> ((big_p(Z1) | big_r(Z1, sk4(Z1)) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))))), rewrite(((big_p(Z1) | big_r(Z1, sk4(Z1)) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) <=> (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))), ((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) <=> (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))))), (((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) <=> ((big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) | (~big_p(a))))), rewrite(((big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))), (((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))))), ((((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) | (~big_r(A2, B2))) <=> (((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) | (~big_r(A2, B2))))), rewrite((((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) | (~big_r(A2, B2))) <=> ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))), ((((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) | (~big_r(A2, B2))) <=> ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(673,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : (((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) | (~big_r(A2, B2))) <=> ![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[672])).
% 0.50/0.67 tff(674,axiom,(![A2: $i, B2: $i, Z1: $i] : (((((big_p(Z1) | big_r(Z1, sk4(Z1))) | big_r(sk2(A2), sk1(A2))) | (~big_p(B2))) | (~big_p(a))) | (~big_r(A2, B2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_21')).
% 0.50/0.67 tff(675,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.50/0.67 tff(676,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[675, 671])).
% 0.50/0.67 tff(677,plain,(
% 0.50/0.67 ![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[676])).
% 0.50/0.67 tff(678,plain,
% 0.50/0.67 (![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[677, 670])).
% 0.50/0.67 tff(679,plain,
% 0.50/0.67 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(680,plain,
% 0.50/0.67 (((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(681,plain,
% 0.50/0.67 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[680])).
% 0.50/0.67 tff(682,plain,
% 0.50/0.67 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[681, 679])).
% 0.50/0.67 tff(683,plain,
% 0.50/0.67 ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(684,plain,
% 0.50/0.67 ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.50/0.67 tff(685,plain,
% 0.50/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[684, 678, 9, 4, 535])).
% 0.50/0.67 tff(686,plain,
% 0.50/0.67 (big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[685, 152, 536])).
% 0.50/0.67 tff(687,plain,
% 0.50/0.67 (^[V1: $i, T1: $i, U1: $i] : refl(((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))) <=> ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(688,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))) <=> ![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[687])).
% 0.50/0.67 tff(689,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))) <=> ![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(690,plain,
% 0.50/0.67 (^[V1: $i, T1: $i, U1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) <=> (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)))), ((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) <=> ((big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1))) | (~big_p(V1))))), rewrite(((big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1))) | (~big_p(V1))) <=> (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)))), ((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) <=> (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))))), (((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) <=> ((big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))) | (~big_p(a))))), rewrite(((big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)))), (((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))))), ((((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) | (~big_r(U1, V1))) <=> (((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))) | (~big_r(U1, V1))))), rewrite((((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1))) | (~big_r(U1, V1))) <=> ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))), ((((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) | (~big_r(U1, V1))) <=> ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(691,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : (((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) | (~big_r(U1, V1))) <=> ![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[690])).
% 0.50/0.67 tff(692,axiom,(![V1: $i, T1: $i, U1: $i] : (((((big_p(T1) | big_r(T1, sk4(T1))) | big_r(U1, sk2(U1))) | (~big_p(V1))) | (~big_p(a))) | (~big_r(U1, V1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_19')).
% 0.50/0.67 tff(693,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.50/0.67 tff(694,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[693, 689])).
% 0.50/0.67 tff(695,plain,(
% 0.50/0.67 ![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[694])).
% 0.50/0.67 tff(696,plain,
% 0.50/0.67 (![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[695, 688])).
% 0.50/0.67 tff(697,plain,
% 0.50/0.67 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(698,plain,
% 0.50/0.67 (((~big_p(a)) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(699,plain,
% 0.50/0.67 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[698])).
% 0.50/0.67 tff(700,plain,
% 0.50/0.67 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[699, 697])).
% 0.50/0.67 tff(701,plain,
% 0.50/0.67 ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(702,plain,
% 0.50/0.67 ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.50/0.67 tff(703,plain,
% 0.50/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[702, 696, 9, 4, 535])).
% 0.50/0.67 tff(704,plain,
% 0.50/0.67 (big_r(sk9, sk2(sk9))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[703, 152, 536])).
% 0.50/0.67 tff(705,plain,
% 0.50/0.67 (^[M2: $i, L2: $i, N2: $i] : refl(((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) <=> ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(706,plain,
% 0.50/0.67 (![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) <=> ![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[705])).
% 0.50/0.67 tff(707,plain,
% 0.50/0.67 (![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) <=> ![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(708,plain,
% 0.50/0.67 (^[M2: $i, L2: $i, N2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) <=> (big_p(L2) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))), ((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) <=> ((big_p(L2) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))))), rewrite(((big_p(L2) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) <=> (big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))), ((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) <=> (big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))))), (((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) <=> ((big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_p(a))))), rewrite(((big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))), (((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))))), ((((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) | (~big_r(M2, N2))) <=> (((~big_p(a)) | big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_r(M2, N2))))), rewrite((((~big_p(a)) | big_p(L2) | (~big_p(N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) | (~big_r(M2, N2))) <=> ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))), ((((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) | (~big_r(M2, N2))) <=> ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(709,plain,
% 0.50/0.68 (![M2: $i, L2: $i, N2: $i] : (((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) | (~big_r(M2, N2))) <=> ![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[708])).
% 0.50/0.68 tff(710,axiom,(![M2: $i, L2: $i, N2: $i] : (((((big_p(L2) | big_p(sk5(M2))) | big_r(sk2(L2), sk1(L2))) | (~big_p(N2))) | (~big_p(a))) | (~big_r(M2, N2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_25')).
% 0.50/0.68 tff(711,plain,
% 0.50/0.68 (![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.50/0.68 tff(712,plain,
% 0.50/0.68 (![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[711, 707])).
% 0.50/0.68 tff(713,plain,(
% 0.50/0.68 ![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.68 inference(skolemize,[status(sab)],[712])).
% 0.50/0.68 tff(714,plain,
% 0.50/0.68 (![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[713, 706])).
% 0.50/0.68 tff(715,plain,
% 0.50/0.68 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(716,plain,
% 0.50/0.68 (((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(717,plain,
% 0.50/0.68 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[716])).
% 0.50/0.68 tff(718,plain,
% 0.50/0.68 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[717, 715])).
% 0.50/0.68 tff(719,plain,
% 0.50/0.68 ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(720,plain,
% 0.50/0.68 ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.50/0.68 tff(721,plain,
% 0.50/0.68 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[720, 714, 9, 4, 535])).
% 0.50/0.68 tff(722,plain,
% 0.50/0.68 (big_p(sk5(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[721, 394, 536])).
% 0.50/0.68 tff(723,plain,
% 0.50/0.68 (^[O2: $i, P2: $i, Q2: $i] : refl(((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) <=> ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(724,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) <=> ![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[723])).
% 0.50/0.68 tff(725,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) <=> ![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(726,plain,
% 0.50/0.68 (^[O2: $i, P2: $i, Q2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) <=> (big_p(O2) | big_r(P2, sk6(P2)) | big_r(sk2(O2), sk1(O2)))), ((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) <=> ((big_p(O2) | big_r(P2, sk6(P2)) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))))), rewrite(((big_p(O2) | big_r(P2, sk6(P2)) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) <=> (big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))), ((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) <=> (big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))))), (((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) <=> ((big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) | (~big_p(a))))), rewrite(((big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))), (((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))))), ((((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) | (~big_r(P2, Q2))) <=> (((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) | (~big_r(P2, Q2))))), rewrite((((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) | (~big_r(P2, Q2))) <=> ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))), ((((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) | (~big_r(P2, Q2))) <=> ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(727,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : (((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) | (~big_r(P2, Q2))) <=> ![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[726])).
% 0.50/0.68 tff(728,axiom,(![O2: $i, P2: $i, Q2: $i] : (((((big_p(O2) | big_r(P2, sk6(P2))) | big_r(sk2(O2), sk1(O2))) | (~big_p(Q2))) | (~big_p(a))) | (~big_r(P2, Q2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_26')).
% 0.50/0.68 tff(729,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.50/0.68 tff(730,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[729, 725])).
% 0.50/0.68 tff(731,plain,(
% 0.50/0.68 ![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(skolemize,[status(sab)],[730])).
% 0.50/0.68 tff(732,plain,
% 0.50/0.68 (![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[731, 724])).
% 0.50/0.68 tff(733,plain,
% 0.50/0.68 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(734,plain,
% 0.50/0.68 (((~big_p(a)) | big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(735,plain,
% 0.50/0.68 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[734])).
% 0.50/0.68 tff(736,plain,
% 0.50/0.68 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[735, 733])).
% 0.50/0.68 tff(737,plain,
% 0.50/0.68 ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(738,plain,
% 0.50/0.68 ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.50/0.68 tff(739,plain,
% 0.50/0.68 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[738, 732, 9, 4, 535])).
% 0.50/0.68 tff(740,plain,
% 0.50/0.68 (big_r(sk9, sk6(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[739, 394, 536])).
% 0.50/0.68 tff(741,plain,
% 0.50/0.68 (^[T2: $i, S2: $i, R2: $i] : refl((big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) <=> (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(742,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) <=> ![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[741])).
% 0.50/0.68 tff(743,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) <=> ![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(744,plain,
% 0.50/0.68 (^[T2: $i, S2: $i, R2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) <=> (big_r(sk2(R2), sk1(R2)) | big_p(R2) | big_r(sk6(S2), sk5(S2)))), ((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) <=> ((big_r(sk2(R2), sk1(R2)) | big_p(R2) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))))), rewrite(((big_r(sk2(R2), sk1(R2)) | big_p(R2) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) <=> (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))), ((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) <=> (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))))), (((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) <=> ((big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) | (~big_p(a))))), rewrite(((big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) | (~big_p(a))) <=> (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))), (((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) <=> (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))))), ((((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) | (~big_r(S2, T2))) <=> ((big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) | (~big_r(S2, T2))))), rewrite(((big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) | (~big_r(S2, T2))) <=> (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))), ((((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) | (~big_r(S2, T2))) <=> (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(745,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) | (~big_r(S2, T2))) <=> ![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[744])).
% 0.50/0.68 tff(746,axiom,(![T2: $i, S2: $i, R2: $i] : (((((big_p(R2) | big_r(sk2(R2), sk1(R2))) | big_r(sk6(S2), sk5(S2))) | (~big_p(T2))) | (~big_p(a))) | (~big_r(S2, T2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_27')).
% 0.50/0.68 tff(747,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.50/0.68 tff(748,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[747, 743])).
% 0.50/0.68 tff(749,plain,(
% 0.50/0.68 ![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(skolemize,[status(sab)],[748])).
% 0.50/0.68 tff(750,plain,
% 0.50/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[749, 742])).
% 0.50/0.68 tff(751,plain,
% 0.50/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(752,plain,
% 0.50/0.68 ((big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(753,plain,
% 0.50/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[752])).
% 0.50/0.68 tff(754,plain,
% 0.50/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[753, 751])).
% 0.50/0.68 tff(755,plain,
% 0.50/0.68 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(756,plain,
% 0.50/0.68 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (~big_p(a)) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.50/0.68 tff(757,plain,
% 0.50/0.68 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[756, 750, 9, 536, 4, 535])).
% 0.50/0.68 tff(758,plain,
% 0.50/0.68 (big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[757, 394])).
% 0.50/0.68 tff(759,plain,
% 0.50/0.68 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(760,plain,
% 0.50/0.68 (((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk6(sk9)))) <=> ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(761,plain,
% 0.50/0.68 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[760])).
% 0.50/0.68 tff(762,plain,
% 0.50/0.68 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[761, 759])).
% 0.50/0.68 tff(763,plain,
% 0.50/0.68 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk9, sk6(sk9))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(764,plain,
% 0.50/0.68 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.50/0.68 tff(765,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[764, 250, 494, 648, 758, 740, 722, 402])).
% 0.50/0.68 tff(766,plain,(big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk7) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(767,plain,
% 0.50/0.68 (big_r(sk2(sk7), sk1(sk7))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[766, 536, 4, 535])).
% 0.50/0.68 tff(768,plain,
% 0.50/0.68 (^[W: $i, V: $i, X: $i] : refl(((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(769,plain,
% 0.50/0.68 (![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> ![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[768])).
% 0.50/0.69 tff(770,plain,
% 0.50/0.69 (![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> ![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(771,plain,
% 0.50/0.69 (^[W: $i, V: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) <=> (big_p(V) | big_r(V, sk2(V)) | big_p(sk5(W)))), ((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) <=> ((big_p(V) | big_r(V, sk2(V)) | big_p(sk5(W))) | (~big_p(X))))), rewrite(((big_p(V) | big_r(V, sk2(V)) | big_p(sk5(W))) | (~big_p(X))) <=> (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W)))), ((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) <=> (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))))), (((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) <=> ((big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))) | (~big_p(a))))), rewrite(((big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W)))), (((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))))), ((((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) | (~big_r(W, X))) <=> (((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))) | (~big_r(W, X))))), rewrite((((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | big_p(sk5(W))) | (~big_r(W, X))) <=> ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))), ((((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) | (~big_r(W, X))) <=> ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(772,plain,
% 0.50/0.69 (![W: $i, V: $i, X: $i] : (((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) | (~big_r(W, X))) <=> ![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[771])).
% 0.50/0.69 tff(773,axiom,(![W: $i, V: $i, X: $i] : (((((big_p(V) | big_p(sk5(W))) | big_r(V, sk2(V))) | (~big_p(X))) | (~big_p(a))) | (~big_r(W, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_10')).
% 0.50/0.69 tff(774,plain,
% 0.50/0.69 (![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.50/0.69 tff(775,plain,
% 0.50/0.69 (![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[774, 770])).
% 0.50/0.69 tff(776,plain,(
% 0.50/0.69 ![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[775])).
% 0.50/0.69 tff(777,plain,
% 0.50/0.69 (![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[776, 769])).
% 0.50/0.69 tff(778,plain,
% 0.50/0.69 (((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))) <=> ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(779,plain,
% 0.50/0.69 ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(780,plain,
% 0.50/0.69 ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.50/0.69 tff(781,plain,
% 0.50/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[780, 777, 9, 4, 535])).
% 0.50/0.69 tff(782,plain,
% 0.50/0.69 (big_p(sk5(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[781, 193, 536])).
% 0.50/0.69 tff(783,plain,
% 0.50/0.69 (^[Z: $i, A1: $i, Y: $i] : refl(((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))) <=> ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(784,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))) <=> ![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[783])).
% 0.50/0.69 tff(785,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))) <=> ![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(786,plain,
% 0.50/0.69 (^[Z: $i, A1: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) <=> (big_p(Y) | big_r(Y, sk2(Y)) | big_r(Z, sk6(Z)))), ((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) <=> ((big_p(Y) | big_r(Y, sk2(Y)) | big_r(Z, sk6(Z))) | (~big_p(A1))))), rewrite(((big_p(Y) | big_r(Y, sk2(Y)) | big_r(Z, sk6(Z))) | (~big_p(A1))) <=> (big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z)))), ((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) <=> (big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))))), (((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) <=> ((big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))) | (~big_p(a))))), rewrite(((big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z)))), (((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))))), ((((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) | (~big_r(Z, A1))) <=> (((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))) | (~big_r(Z, A1))))), rewrite((((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_p(A1)) | big_r(Z, sk6(Z))) | (~big_r(Z, A1))) <=> ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))), ((((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) | (~big_r(Z, A1))) <=> ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(787,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : (((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) | (~big_r(Z, A1))) <=> ![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[786])).
% 0.50/0.69 tff(788,axiom,(![Z: $i, A1: $i, Y: $i] : (((((big_p(Y) | big_r(Z, sk6(Z))) | big_r(Y, sk2(Y))) | (~big_p(A1))) | (~big_p(a))) | (~big_r(Z, A1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_11')).
% 0.50/0.69 tff(789,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.50/0.69 tff(790,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[789, 785])).
% 0.50/0.69 tff(791,plain,(
% 0.50/0.69 ![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[790])).
% 0.50/0.69 tff(792,plain,
% 0.50/0.69 (![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[791, 784])).
% 0.50/0.69 tff(793,plain,
% 0.50/0.69 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(794,plain,
% 0.50/0.69 (((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(795,plain,
% 0.50/0.69 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[794])).
% 0.50/0.69 tff(796,plain,
% 0.50/0.69 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[795, 793])).
% 0.50/0.69 tff(797,plain,
% 0.50/0.69 ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(798,plain,
% 0.50/0.69 ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.50/0.69 tff(799,plain,
% 0.50/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[798, 792, 9, 4, 535])).
% 0.50/0.69 tff(800,plain,
% 0.50/0.69 (big_r(sk9, sk6(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[799, 193, 536])).
% 0.50/0.69 tff(801,plain,
% 0.50/0.69 (^[B1: $i, D1: $i, C1: $i] : refl(((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) <=> ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(802,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) <=> ![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[801])).
% 0.50/0.69 tff(803,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) <=> ![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(804,plain,
% 0.50/0.69 (^[B1: $i, D1: $i, C1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) <=> (big_p(B1) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))), ((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) <=> ((big_p(B1) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_p(D1))))), rewrite(((big_p(B1) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_p(D1))) <=> (big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))), ((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) <=> (big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))))), (((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) <=> ((big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_p(a))))), rewrite(((big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))), (((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))))), ((((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) | (~big_r(C1, D1))) <=> (((~big_p(a)) | big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_r(C1, D1))))), rewrite((((~big_p(a)) | big_p(B1) | (~big_p(D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) | (~big_r(C1, D1))) <=> ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))), ((((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) | (~big_r(C1, D1))) <=> ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(805,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : (((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) | (~big_r(C1, D1))) <=> ![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[804])).
% 0.50/0.69 tff(806,axiom,(![B1: $i, D1: $i, C1: $i] : (((((big_p(B1) | big_r(B1, sk2(B1))) | big_r(sk6(C1), sk5(C1))) | (~big_p(D1))) | (~big_p(a))) | (~big_r(C1, D1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_12')).
% 0.50/0.69 tff(807,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.50/0.69 tff(808,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[807, 803])).
% 0.50/0.69 tff(809,plain,(
% 0.50/0.69 ![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[808])).
% 0.50/0.69 tff(810,plain,
% 0.50/0.69 (![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[809, 802])).
% 0.50/0.69 tff(811,plain,
% 0.50/0.69 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(812,plain,
% 0.50/0.69 (((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7))) <=> ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(813,plain,
% 0.50/0.69 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[812])).
% 0.50/0.69 tff(814,plain,
% 0.50/0.69 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[813, 811])).
% 0.50/0.69 tff(815,plain,
% 0.50/0.69 ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(816,plain,
% 0.50/0.69 ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (~big_p(a)) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.50/0.69 tff(817,plain,
% 0.50/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[816, 810, 9, 4, 535])).
% 0.50/0.69 tff(818,plain,
% 0.50/0.69 (big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[817, 193, 536])).
% 0.50/0.69 tff(819,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[764, 250, 232, 648, 818, 800, 782, 450])).
% 0.50/0.69 tff(820,plain,(big_r(sk7, sk2(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(821,plain,
% 0.50/0.69 (big_r(sk7, sk2(sk7))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[820, 4, 536, 535])).
% 0.50/0.69 tff(822,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[280, 250, 821, 767, 704, 686, 668, 666])).
% 0.50/0.69 tff(823,plain,(big_r(sk7, sk4(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(824,plain,
% 0.50/0.69 (big_r(sk7, sk4(sk7))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[823, 4, 536, 535])).
% 0.50/0.69 tff(825,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[764, 250, 824, 648, 590, 572, 554, 27])).
% 0.50/0.69 tff(826,plain,(big_p(sk1(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(827,plain,
% 0.50/0.69 (big_p(sk1(sk7))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[826, 4, 534, 535])).
% 0.50/0.69 tff(828,plain,
% 0.50/0.69 (big_r(sk2(sk7), sk1(sk7))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[766, 534, 4, 535])).
% 0.50/0.69 tff(829,plain,
% 0.50/0.69 (big_r(sk7, sk2(sk7))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[820, 4, 534, 535])).
% 0.50/0.69 tff(830,assumption,(~big_r(sk9, sk6(sk9))), introduced(assumption)).
% 0.50/0.69 tff(831,plain,
% 0.50/0.69 (^[E3: $i, F3: $i, D3: $i, C3: $i] : refl(((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(832,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))) <=> ![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[831])).
% 0.50/0.69 tff(833,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))) <=> ![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(834,plain,
% 0.50/0.69 (^[E3: $i, F3: $i, D3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) <=> (big_p(sk1(C3)) | big_r(D3, sk6(D3)) | (~big_p(E3)))), ((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) <=> ((big_p(sk1(C3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_p(F3))))), rewrite(((big_p(sk1(C3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_p(F3))) <=> (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)))), ((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) <=> (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))))), (((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) <=> ((big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_p(a))))), rewrite(((big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)))), (((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))))), ((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) <=> (((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_r(D3, E3))))), rewrite((((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3))) | (~big_r(D3, E3))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)) | (~big_r(D3, E3)))), ((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)) | (~big_r(D3, E3))))), (((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) | (~big_r(C3, F3))) <=> (((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)) | (~big_r(D3, E3))) | (~big_r(C3, F3))))), rewrite((((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_p(E3)) | (~big_r(D3, E3))) | (~big_r(C3, F3))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))), (((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) | (~big_r(C3, F3))) <=> ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(835,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) | (~big_r(C3, F3))) <=> ![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[834])).
% 0.50/0.69 tff(836,axiom,(![E3: $i, F3: $i, D3: $i, C3: $i] : ((((((big_p(sk1(C3)) | big_r(D3, sk6(D3))) | (~big_p(E3))) | (~big_p(F3))) | (~big_p(a))) | (~big_r(D3, E3))) | (~big_r(C3, F3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_30')).
% 0.50/0.69 tff(837,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.50/0.69 tff(838,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[837, 833])).
% 0.50/0.69 tff(839,plain,(
% 0.50/0.69 ![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[838])).
% 0.50/0.69 tff(840,plain,
% 0.50/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[839, 832])).
% 0.50/0.69 tff(841,plain,
% 0.50/0.69 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(842,plain,
% 0.50/0.69 (((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(843,plain,
% 0.50/0.69 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[842])).
% 0.50/0.69 tff(844,plain,
% 0.50/0.69 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[843, 841])).
% 0.50/0.69 tff(845,plain,
% 0.50/0.69 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(846,plain,
% 0.50/0.69 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.50/0.70 tff(847,plain,
% 0.50/0.70 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[846, 840, 9, 535])).
% 0.50/0.70 tff(848,plain,
% 0.50/0.70 (big_p(sk1(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[847, 830, 536])).
% 0.50/0.70 tff(849,assumption,(big_p(sk1(sk7))), introduced(assumption)).
% 0.50/0.70 tff(850,plain,
% 0.50/0.70 (^[O3: $i, P3: $i, R3: $i, Q3: $i] : refl(((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(851,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) <=> ![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[850])).
% 0.50/0.70 tff(852,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) <=> ![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(853,plain,
% 0.50/0.70 (^[O3: $i, P3: $i, R3: $i, Q3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) <=> (big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)))), (((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) <=> ((big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(Q3))))), rewrite(((big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(Q3))) <=> ((~big_p(Q3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)))), (((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) <=> ((~big_p(Q3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))))), ((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) <=> (((~big_p(Q3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(R3))))), rewrite((((~big_p(Q3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(R3))) <=> ((~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)))), ((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) <=> ((~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))))), (((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) <=> (((~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(a))))), rewrite((((~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)))), (((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))))), ((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) <=> (((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_r(O3, Q3))))), rewrite((((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3))) | (~big_r(O3, Q3))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))), ((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))))), (((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) | (~big_r(P3, R3))) <=> (((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) | (~big_r(P3, R3))))), rewrite((((~big_p(a)) | (~big_p(Q3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) | (~big_r(P3, R3))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))), (((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) | (~big_r(P3, R3))) <=> ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(854,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) | (~big_r(P3, R3))) <=> ![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[853])).
% 0.50/0.70 tff(855,axiom,(![O3: $i, P3: $i, R3: $i, Q3: $i] : ((((((big_r(O3, sk6(O3)) | big_r(sk2(P3), sk1(P3))) | (~big_p(Q3))) | (~big_p(R3))) | (~big_p(a))) | (~big_r(O3, Q3))) | (~big_r(P3, R3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_33')).
% 0.50/0.70 tff(856,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.50/0.70 tff(857,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[856, 852])).
% 0.50/0.70 tff(858,plain,(
% 0.50/0.70 ![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[857])).
% 0.50/0.70 tff(859,plain,
% 0.50/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[858, 851])).
% 0.50/0.70 tff(860,plain,
% 0.50/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(861,plain,
% 0.50/0.70 (((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(862,plain,
% 0.50/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[861])).
% 0.50/0.70 tff(863,plain,
% 0.50/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(transitivity,[status(thm)],[862, 860])).
% 0.50/0.70 tff(864,plain,
% 0.50/0.70 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(865,plain,
% 0.50/0.70 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.50/0.70 tff(866,plain,
% 0.50/0.70 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[865, 859, 9, 535])).
% 0.50/0.70 tff(867,plain,
% 0.50/0.70 (big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[866, 830, 536])).
% 0.50/0.70 tff(868,plain,
% 0.50/0.70 (^[G3: $i, H3: $i, I3: $i, J3: $i] : refl(((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(869,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) <=> ![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[868])).
% 0.50/0.70 tff(870,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) <=> ![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(871,plain,
% 0.50/0.70 (^[G3: $i, H3: $i, I3: $i, J3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) <=> (big_r(H3, sk2(H3)) | big_r(G3, sk6(G3)))), (((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) <=> ((big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(I3))))), rewrite(((big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(I3))) <=> ((~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3)))), (((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) <=> ((~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))))), ((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) <=> (((~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(J3))))), rewrite((((~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(J3))) <=> ((~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3)))), ((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) <=> ((~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))))), (((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) <=> (((~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(a))))), rewrite((((~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3)))), (((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))))), ((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) <=> (((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_r(G3, I3))))), rewrite((((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | big_r(G3, sk6(G3))) | (~big_r(G3, I3))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))), ((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))))), (((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) | (~big_r(H3, J3))) <=> (((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) | (~big_r(H3, J3))))), rewrite((((~big_p(a)) | (~big_p(J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) | (~big_r(H3, J3))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))), (((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) | (~big_r(H3, J3))) <=> ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(872,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) | (~big_r(H3, J3))) <=> ![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[871])).
% 0.50/0.70 tff(873,axiom,(![G3: $i, H3: $i, I3: $i, J3: $i] : ((((((big_r(G3, sk6(G3)) | big_r(H3, sk2(H3))) | (~big_p(I3))) | (~big_p(J3))) | (~big_p(a))) | (~big_r(G3, I3))) | (~big_r(H3, J3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_31')).
% 0.50/0.70 tff(874,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.50/0.70 tff(875,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[874, 870])).
% 0.50/0.70 tff(876,plain,(
% 0.50/0.70 ![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[875])).
% 0.50/0.70 tff(877,plain,
% 0.50/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[876, 869])).
% 0.50/0.70 tff(878,plain,
% 0.50/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(879,plain,
% 0.50/0.70 (((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(880,plain,
% 0.50/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[879])).
% 0.50/0.70 tff(881,plain,
% 0.50/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(transitivity,[status(thm)],[880, 878])).
% 0.50/0.70 tff(882,plain,
% 0.50/0.70 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(883,plain,
% 0.50/0.70 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.50/0.70 tff(884,plain,
% 0.50/0.70 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[883, 877, 9, 535])).
% 0.50/0.70 tff(885,plain,
% 0.50/0.70 (big_r(sk9, sk2(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[884, 830, 536])).
% 0.50/0.70 tff(886,assumption,(big_r(sk2(sk7), sk1(sk7))), introduced(assumption)).
% 0.50/0.70 tff(887,assumption,(big_r(sk7, sk2(sk7))), introduced(assumption)).
% 0.50/0.70 tff(888,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[280, 250, 887, 886, 885, 867, 849, 848])).
% 0.50/0.70 tff(889,plain,(big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.70 tff(890,plain,
% 0.50/0.70 (big_r(sk9, sk6(sk9))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[889, 829, 828, 827, 534, 535])).
% 0.50/0.70 tff(891,plain,
% 0.50/0.70 (^[Y1: $i, W1: $i, X1: $i] : refl((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(892,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))) <=> ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[891])).
% 0.50/0.70 tff(893,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))) <=> ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(894,plain,
% 0.50/0.70 (^[Y1: $i, W1: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1))), ((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) <=> ((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1)) | (~big_p(Y1))))), rewrite(((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1)) | (~big_p(Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)))), ((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1))))), (((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) <=> ((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1))) | (~big_p(a))))), rewrite(((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1))) | (~big_p(a))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)))), (((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1))))), ((((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) | (~big_r(X1, Y1))) <=> ((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1))) | (~big_r(X1, Y1))))), rewrite(((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1))) | (~big_r(X1, Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))), ((((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) | (~big_r(X1, Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(895,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) | (~big_r(X1, Y1))) <=> ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[894])).
% 0.50/0.70 tff(896,axiom,(![Y1: $i, W1: $i, X1: $i] : (((((big_p(W1) | big_p(sk3(W1))) | big_r(sk2(X1), sk1(X1))) | (~big_p(Y1))) | (~big_p(a))) | (~big_r(X1, Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_20')).
% 0.50/0.70 tff(897,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.50/0.70 tff(898,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[897, 893])).
% 0.50/0.70 tff(899,plain,(
% 0.50/0.70 ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[898])).
% 0.50/0.70 tff(900,plain,
% 0.50/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[899, 892])).
% 0.50/0.70 tff(901,plain,
% 0.50/0.70 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(902,plain,
% 0.50/0.70 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(903,plain,
% 0.50/0.71 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | ((~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[902])).
% 0.50/0.71 tff(904,plain,
% 0.50/0.71 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[903, 901])).
% 0.50/0.71 tff(905,plain,
% 0.50/0.71 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | (~big_p(a)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(906,plain,
% 0.50/0.71 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (~big_p(a)) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.50/0.71 tff(907,plain,
% 0.50/0.71 (big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[906, 900, 9, 536, 4, 535])).
% 0.50/0.71 tff(908,plain,
% 0.50/0.71 (big_p(sk3(sk7))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[907, 91])).
% 0.50/0.71 tff(909,plain,
% 0.50/0.71 (^[L3: $i, N3: $i, M3: $i, K3: $i] : refl(((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(910,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))) <=> ![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[909])).
% 0.50/0.71 tff(911,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))) <=> ![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(912,plain,
% 0.50/0.71 (^[L3: $i, N3: $i, M3: $i, K3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) <=> ((~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3)))), ((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) <=> (((~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(N3))))), rewrite((((~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(N3))) <=> ((~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3)))), ((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) <=> ((~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))))), (((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) <=> (((~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(a))))), rewrite((((~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3)))), (((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))))), ((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) <=> (((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_r(K3, M3))))), rewrite((((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_r(K3, M3))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3)))), ((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))))), (((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) | (~big_r(L3, N3))) <=> (((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_r(L3, N3))))), rewrite((((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_r(L3, N3))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))), (((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) | (~big_r(L3, N3))) <=> ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(913,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) | (~big_r(L3, N3))) <=> ![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[912])).
% 0.50/0.71 tff(914,axiom,(![L3: $i, N3: $i, M3: $i, K3: $i] : ((((((big_p(sk5(K3)) | big_r(sk2(L3), sk1(L3))) | (~big_p(M3))) | (~big_p(N3))) | (~big_p(a))) | (~big_r(K3, M3))) | (~big_r(L3, N3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_32')).
% 0.50/0.71 tff(915,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.50/0.71 tff(916,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[915, 911])).
% 0.50/0.71 tff(917,plain,(
% 0.50/0.71 ![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(skolemize,[status(sab)],[916])).
% 0.50/0.71 tff(918,plain,
% 0.50/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[917, 910])).
% 0.50/0.71 tff(919,plain,
% 0.50/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(920,plain,
% 0.50/0.71 (((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(921,plain,
% 0.50/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[920])).
% 0.50/0.71 tff(922,plain,
% 0.50/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[921, 919])).
% 0.50/0.71 tff(923,plain,
% 0.50/0.71 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(924,plain,
% 0.50/0.71 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.50/0.71 tff(925,plain,
% 0.50/0.71 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[924, 918, 9, 535])).
% 0.50/0.71 tff(926,plain,
% 0.50/0.71 (big_p(sk5(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[925, 91, 536])).
% 0.50/0.71 tff(927,plain,
% 0.50/0.71 (big_p(sk1(sk7))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[826, 4, 536, 535])).
% 0.50/0.71 tff(928,plain,
% 0.50/0.71 (big_r(sk9, sk6(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[889, 821, 767, 927, 536, 535])).
% 0.50/0.71 tff(929,plain,
% 0.50/0.71 (^[A4: $i, C4: $i, B4: $i, D4: $i] : refl(((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))) <=> ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(930,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))) <=> ![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[929])).
% 0.50/0.71 tff(931,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))) <=> ![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(932,plain,
% 0.50/0.71 (^[A4: $i, C4: $i, B4: $i, D4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) <=> ((~big_p(C4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)))), ((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) <=> (((~big_p(C4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_p(D4))))), rewrite((((~big_p(C4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_p(D4))) <=> ((~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)))), ((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) <=> ((~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))))), (((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) <=> (((~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_p(a))))), rewrite((((~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)))), (((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))))), ((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) <=> (((~big_p(a)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_r(B4, C4))))), rewrite((((~big_p(a)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_r(B4, C4))) <=> ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)))), ((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) <=> ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))))), (((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) | (~big_r(A4, D4))) <=> (((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_r(A4, D4))))), rewrite((((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4))) | (~big_r(A4, D4))) <=> ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))), (((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) | (~big_r(A4, D4))) <=> ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(933,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) | (~big_r(A4, D4))) <=> ![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[932])).
% 0.50/0.71 tff(934,axiom,(![A4: $i, C4: $i, B4: $i, D4: $i] : ((((((big_r(sk2(A4), sk1(A4)) | big_r(sk6(B4), sk5(B4))) | (~big_p(C4))) | (~big_p(D4))) | (~big_p(a))) | (~big_r(B4, C4))) | (~big_r(A4, D4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_36')).
% 0.50/0.71 tff(935,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.50/0.71 tff(936,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[935, 931])).
% 0.50/0.71 tff(937,plain,(
% 0.50/0.71 ![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(skolemize,[status(sab)],[936])).
% 0.50/0.71 tff(938,plain,
% 0.50/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[937, 930])).
% 0.50/0.71 tff(939,plain,
% 0.50/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(940,plain,
% 0.50/0.71 (((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(941,plain,
% 0.50/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[940])).
% 0.50/0.71 tff(942,plain,
% 0.50/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[941, 939])).
% 0.50/0.71 tff(943,plain,
% 0.50/0.71 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(944,plain,
% 0.50/0.71 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[943, 942])).
% 0.50/0.71 tff(945,plain,
% 0.50/0.71 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[944, 938, 9, 535])).
% 0.50/0.71 tff(946,plain,
% 0.50/0.71 (big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[945, 91, 536])).
% 0.50/0.71 tff(947,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[764, 250, 824, 648, 946, 928, 926, 908])).
% 0.50/0.71 tff(948,plain,(big_r(sk2(sk9), sk1(sk9)) | (~big_p(sk10)) | big_p(sk7) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(949,plain,
% 0.50/0.71 (big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[948, 534, 4, 535])).
% 0.50/0.71 tff(950,assumption,(~big_r(sk6(sk9), sk5(sk9))), introduced(assumption)).
% 0.50/0.71 tff(951,plain,
% 0.50/0.71 (^[T3: $i, S3: $i, U3: $i, V3: $i] : refl(((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(952,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) <=> ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[951])).
% 0.50/0.71 tff(953,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) <=> ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(954,plain,
% 0.50/0.71 (^[T3: $i, S3: $i, U3: $i, V3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) <=> (big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3)))), ((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) <=> ((big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(V3))))), rewrite(((big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(V3))) <=> ((~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3)))), ((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) <=> ((~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))))), (((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) <=> (((~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(a))))), rewrite((((~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3)))), (((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))))), ((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) <=> (((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_r(T3, U3))))), rewrite((((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | big_r(sk6(T3), sk5(T3))) | (~big_r(T3, U3))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))), ((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))))), (((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) | (~big_r(S3, V3))) <=> (((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) | (~big_r(S3, V3))))), rewrite((((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) | (~big_r(S3, V3))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))), (((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) | (~big_r(S3, V3))) <=> ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))))),
% 0.50/0.71 inference(bind,[status(th)],[])).
% 0.50/0.71 tff(955,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) | (~big_r(S3, V3))) <=> ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(quant_intro,[status(thm)],[954])).
% 0.50/0.71 tff(956,axiom,(![T3: $i, S3: $i, U3: $i, V3: $i] : ((((((big_p(sk1(S3)) | big_r(sk6(T3), sk5(T3))) | (~big_p(U3))) | (~big_p(V3))) | (~big_p(a))) | (~big_r(T3, U3))) | (~big_r(S3, V3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_34')).
% 0.50/0.71 tff(957,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.50/0.71 tff(958,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[957, 953])).
% 0.50/0.71 tff(959,plain,(
% 0.50/0.71 ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(skolemize,[status(sab)],[958])).
% 0.50/0.71 tff(960,plain,
% 0.50/0.71 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[959, 952])).
% 0.50/0.71 tff(961,plain,
% 0.50/0.71 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(962,plain,
% 0.50/0.71 (((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(963,plain,
% 0.50/0.71 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[962])).
% 0.50/0.71 tff(964,plain,
% 0.50/0.71 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[963, 961])).
% 0.50/0.71 tff(965,plain,
% 0.50/0.71 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(966,plain,
% 0.50/0.72 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.50/0.72 tff(967,plain,
% 0.50/0.72 ((~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[966, 960, 9, 535])).
% 0.50/0.72 tff(968,plain,
% 0.50/0.72 (big_p(sk1(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[967, 950, 536])).
% 0.50/0.72 tff(969,plain,
% 0.50/0.72 (^[Z3: $i, Y3: $i, X3: $i, W3: $i] : refl(((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))))),
% 0.50/0.72 inference(bind,[status(th)],[])).
% 0.50/0.72 tff(970,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))) <=> ![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(quant_intro,[status(thm)],[969])).
% 0.50/0.72 tff(971,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))) <=> ![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(972,plain,
% 0.50/0.72 (^[Z3: $i, Y3: $i, X3: $i, W3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) <=> (big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3)))), (((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) <=> ((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))))), rewrite(((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) <=> (big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)))), (((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) <=> (big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3))))), ((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) <=> ((big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Z3))))), rewrite(((big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Z3))) <=> (big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)))), ((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) <=> (big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))))), (((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) <=> ((big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_p(a))))), rewrite(((big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)))), (((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))))), ((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) <=> (((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_r(X3, Y3))))), rewrite((((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_r(X3, Y3))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)))), ((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))))), (((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) | (~big_r(W3, Z3))) <=> (((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_r(W3, Z3))))), rewrite((((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3))) | (~big_r(W3, Z3))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))), (((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) | (~big_r(W3, Z3))) <=> ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))))),
% 0.50/0.72 inference(bind,[status(th)],[])).
% 0.50/0.72 tff(973,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) | (~big_r(W3, Z3))) <=> ![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(quant_intro,[status(thm)],[972])).
% 0.50/0.72 tff(974,axiom,(![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((((((big_r(W3, sk2(W3)) | big_r(sk6(X3), sk5(X3))) | (~big_p(Y3))) | (~big_p(Z3))) | (~big_p(a))) | (~big_r(X3, Y3))) | (~big_r(W3, Z3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_35')).
% 0.50/0.72 tff(975,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.50/0.72 tff(976,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[975, 971])).
% 0.50/0.72 tff(977,plain,(
% 0.50/0.72 ![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(skolemize,[status(sab)],[976])).
% 0.50/0.72 tff(978,plain,
% 0.50/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[977, 970])).
% 0.50/0.72 tff(979,plain,
% 0.50/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(980,plain,
% 0.50/0.72 (((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(981,plain,
% 0.50/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[980])).
% 0.50/0.72 tff(982,plain,
% 0.50/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[981, 979])).
% 0.50/0.72 tff(983,plain,
% 0.50/0.72 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(984,plain,
% 0.50/0.72 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.50/0.72 tff(985,plain,
% 0.50/0.72 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[984, 978, 9, 535])).
% 0.50/0.72 tff(986,plain,
% 0.50/0.72 (big_r(sk9, sk2(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[985, 950, 536])).
% 0.50/0.72 tff(987,assumption,(big_r(sk2(sk9), sk1(sk9))), introduced(assumption)).
% 0.50/0.72 tff(988,plain,
% 0.50/0.72 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[280, 250, 887, 886, 987, 849])).
% 0.50/0.72 tff(989,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[988, 986, 968])).
% 0.50/0.72 tff(990,plain,(big_r(sk6(sk9), sk5(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(991,plain,
% 0.50/0.72 (big_r(sk6(sk9), sk5(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[990, 829, 828, 949, 827, 534, 535])).
% 0.50/0.72 tff(992,plain,
% 0.50/0.72 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(993,plain,
% 0.50/0.72 (((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk6(sk9)))) <=> ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(994,plain,
% 0.50/0.72 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7)))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[993])).
% 0.50/0.72 tff(995,plain,
% 0.50/0.72 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.50/0.72 inference(transitivity,[status(thm)],[994, 992])).
% 0.50/0.72 tff(996,plain,
% 0.50/0.72 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk9, sk6(sk9))))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(997,plain,
% 0.50/0.72 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk2(sk7)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[996, 995])).
% 0.50/0.72 tff(998,plain,
% 0.50/0.72 (~big_p(sk5(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[997, 250, 829, 828, 827, 991, 890])).
% 0.50/0.72 tff(999,plain,
% 0.50/0.72 (^[U2: $i, W2: $i, X2: $i, V2: $i] : refl(((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))))),
% 0.50/0.72 inference(bind,[status(th)],[])).
% 0.50/0.72 tff(1000,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(quant_intro,[status(thm)],[999])).
% 0.50/0.72 tff(1001,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(1002,plain,
% 0.50/0.72 (^[U2: $i, W2: $i, X2: $i, V2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) <=> ((~big_p(W2)) | big_p(sk5(V2)) | big_p(sk1(U2)))), ((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) <=> (((~big_p(W2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_p(X2))))), rewrite((((~big_p(W2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_p(X2))) <=> ((~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))), ((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) <=> ((~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))))), (((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) <=> (((~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_p(a))))), rewrite((((~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))), (((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))))), ((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) <=> (((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_r(V2, W2))))), rewrite((((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_r(V2, W2))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | big_p(sk5(V2)) | big_p(sk1(U2)))), ((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | big_p(sk5(V2)) | big_p(sk1(U2))))), (((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) | (~big_r(U2, X2))) <=> (((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_r(U2, X2))))), rewrite((((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | big_p(sk5(V2)) | big_p(sk1(U2))) | (~big_r(U2, X2))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))), (((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) | (~big_r(U2, X2))) <=> ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))))),
% 0.50/0.72 inference(bind,[status(th)],[])).
% 0.50/0.72 tff(1003,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) | (~big_r(U2, X2))) <=> ![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(quant_intro,[status(thm)],[1002])).
% 0.50/0.72 tff(1004,axiom,(![U2: $i, W2: $i, X2: $i, V2: $i] : ((((((big_p(sk1(U2)) | big_p(sk5(V2))) | (~big_p(W2))) | (~big_p(X2))) | (~big_p(a))) | (~big_r(V2, W2))) | (~big_r(U2, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_28')).
% 0.50/0.72 tff(1005,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.50/0.72 tff(1006,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[1005, 1001])).
% 0.50/0.72 tff(1007,plain,(
% 0.50/0.72 ![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(skolemize,[status(sab)],[1006])).
% 0.50/0.72 tff(1008,plain,
% 0.50/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[1007, 1000])).
% 0.50/0.72 tff(1009,plain,
% 0.50/0.72 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(1010,plain,
% 0.50/0.72 (((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(1011,plain,
% 0.50/0.72 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[1010])).
% 0.50/0.72 tff(1012,plain,
% 0.50/0.72 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.50/0.72 tff(1013,plain,
% 0.50/0.72 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(1014,plain,
% 0.50/0.72 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.50/0.72 tff(1015,plain,
% 0.50/0.72 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[1014, 1008, 9, 535])).
% 0.50/0.72 tff(1016,plain,
% 0.50/0.72 (big_p(sk1(sk9))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[1015, 998, 534])).
% 0.50/0.72 tff(1017,plain,
% 0.50/0.72 (^[A3: $i, Y2: $i, B3: $i, Z2: $i] : refl(((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))))),
% 0.50/0.72 inference(bind,[status(th)],[])).
% 0.50/0.72 tff(1018,plain,
% 0.50/0.72 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> ![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.72 inference(quant_intro,[status(thm)],[1017])).
% 0.50/0.72 tff(1019,plain,
% 0.50/0.72 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> ![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(1020,plain,
% 0.50/0.72 (^[A3: $i, Y2: $i, B3: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) <=> (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(A3)))), ((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) <=> ((big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(A3))) | (~big_p(B3))))), rewrite(((big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(A3))) | (~big_p(B3))) <=> (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3)))), ((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) <=> (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))))), (((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) <=> ((big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))) | (~big_p(a))))), rewrite(((big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3)))), (((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))))), ((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) <=> (((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))) | (~big_r(Y2, A3))))), rewrite((((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_p(A3))) | (~big_r(Y2, A3))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))), ((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Y2, A3)) | (~big_p(A3))))), (((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) | (~big_r(Z2, B3))) <=> (((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) | (~big_r(Z2, B3))))), rewrite((((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) | (~big_r(Z2, B3))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))), (((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) | (~big_r(Z2, B3))) <=> ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))))),
% 0.50/0.73 inference(bind,[status(th)],[])).
% 0.50/0.73 tff(1021,plain,
% 0.50/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) | (~big_r(Z2, B3))) <=> ![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.73 inference(quant_intro,[status(thm)],[1020])).
% 0.50/0.73 tff(1022,axiom,(![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((((((big_p(sk5(Y2)) | big_r(Z2, sk2(Z2))) | (~big_p(A3))) | (~big_p(B3))) | (~big_p(a))) | (~big_r(Y2, A3))) | (~big_r(Z2, B3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_29')).
% 0.50/0.73 tff(1023,plain,
% 0.50/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.50/0.73 tff(1024,plain,
% 0.50/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 0.50/0.73 tff(1025,plain,(
% 0.50/0.73 ![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.73 inference(skolemize,[status(sab)],[1024])).
% 0.50/0.73 tff(1026,plain,
% 0.50/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 0.50/0.73 tff(1027,plain,
% 0.50/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1028,plain,
% 0.50/0.73 (((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1029,plain,
% 0.50/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))))),
% 0.50/0.73 inference(monotonicity,[status(thm)],[1028])).
% 0.50/0.73 tff(1030,plain,
% 0.50/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.50/0.73 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.50/0.73 tff(1031,plain,
% 0.50/0.73 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.50/0.73 inference(quant_inst,[status(thm)],[])).
% 0.50/0.73 tff(1032,plain,
% 0.50/0.73 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.50/0.73 tff(1033,plain,
% 0.50/0.73 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1032, 1026, 9, 535])).
% 0.50/0.73 tff(1034,plain,
% 0.50/0.73 (big_r(sk9, sk2(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1033, 998, 534])).
% 0.50/0.73 tff(1035,plain,
% 0.50/0.73 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[280, 250, 829, 828, 949, 827])).
% 0.50/0.73 tff(1036,plain,
% 0.50/0.73 ($false),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1035, 1034, 1016])).
% 0.50/0.73 tff(1037,plain,(big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.73 tff(1038,plain,
% 0.50/0.73 ($false),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1037, 491, 4, 447])).
% 0.50/0.73 tff(1039,plain,(big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.73 tff(1040,assumption,(~big_p(sk3(sk9))), introduced(assumption)).
% 0.50/0.73 tff(1041,plain,
% 0.50/0.73 (big_p(sk1(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[444, 1040])).
% 0.50/0.73 tff(1042,assumption,(~big_r(sk7, sk8)), introduced(assumption)).
% 0.50/0.73 tff(1043,plain,
% 0.50/0.73 (big_p(sk7)),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[446, 5])).
% 0.50/0.73 tff(1044,plain,
% 0.50/0.73 (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[114, 101, 9, 5])).
% 0.50/0.73 tff(1045,plain,
% 0.50/0.73 (big_p(sk3(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1044, 91])).
% 0.50/0.73 tff(1046,assumption,(big_p(sk7)), introduced(assumption)).
% 0.50/0.73 tff(1047,plain,
% 0.50/0.73 (big_r(sk2(sk9), sk1(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[150, 377])).
% 0.50/0.73 tff(1048,plain,
% 0.50/0.73 (^[G4: $i, H4: $i] : refl(((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4))) <=> ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4))))),
% 0.50/0.73 inference(bind,[status(th)],[])).
% 0.50/0.73 tff(1049,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4))) <=> ![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(quant_intro,[status(thm)],[1048])).
% 0.50/0.73 tff(1050,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4))) <=> ![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1051,plain,
% 0.50/0.73 (^[G4: $i, H4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_r(sk7, sk8) | (~big_p(G4))) <=> ((~big_p(G4)) | big_r(sk7, sk8))), (((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) <=> (((~big_p(G4)) | big_r(sk7, sk8)) | (~big_p(sk7))))), rewrite((((~big_p(G4)) | big_r(sk7, sk8)) | (~big_p(sk7))) <=> ((~big_p(G4)) | big_r(sk7, sk8) | (~big_p(sk7)))), (((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) <=> ((~big_p(G4)) | big_r(sk7, sk8) | (~big_p(sk7))))), ((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) <=> (((~big_p(G4)) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_r(H4, G4))))), rewrite((((~big_p(G4)) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_r(H4, G4))) <=> ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)))), ((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) <=> ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7))))), (((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) | (~big_r(sk9, H4))) <=> (((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_r(sk9, H4))))), rewrite((((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_r(sk9, H4))) <=> ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))), (((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) | (~big_r(sk9, H4))) <=> ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))))),
% 0.50/0.73 inference(bind,[status(th)],[])).
% 0.50/0.73 tff(1052,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) | (~big_r(sk9, H4))) <=> ![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(quant_intro,[status(thm)],[1051])).
% 0.50/0.73 tff(1053,axiom,(![G4: $i, H4: $i] : ((((big_r(sk7, sk8) | (~big_p(G4))) | (~big_p(sk7))) | (~big_r(H4, G4))) | (~big_r(sk9, H4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_43')).
% 0.50/0.73 tff(1054,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.50/0.73 tff(1055,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 0.50/0.73 tff(1056,plain,(
% 0.50/0.73 ![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(skolemize,[status(sab)],[1055])).
% 0.50/0.73 tff(1057,plain,
% 0.50/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1056, 1049])).
% 0.50/0.73 tff(1058,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1059,plain,
% 0.50/0.73 (((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9)))) <=> (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1060,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))))),
% 0.50/0.73 inference(monotonicity,[status(thm)],[1059])).
% 0.50/0.73 tff(1061,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.50/0.73 inference(transitivity,[status(thm)],[1060, 1058])).
% 0.50/0.73 tff(1062,plain,
% 0.50/0.73 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))),
% 0.50/0.73 inference(quant_inst,[status(thm)],[])).
% 0.50/0.73 tff(1063,plain,
% 0.50/0.73 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.50/0.73 tff(1064,plain,
% 0.50/0.73 (~big_p(sk3(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1063, 1046, 1042, 1057, 322, 53])).
% 0.50/0.73 tff(1065,plain,
% 0.50/0.73 ($false),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[328, 217, 9, 5, 3, 1064])).
% 0.50/0.73 tff(1066,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9) | (~big_p(sk7)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.73 tff(1067,plain,
% 0.50/0.73 (big_r(sk9, sk2(sk9))),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[1066, 5, 1046, 1042])).
% 0.50/0.73 tff(1068,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1069,plain,
% 0.50/0.73 (((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9)))) <=> (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(1070,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))))),
% 0.50/0.73 inference(monotonicity,[status(thm)],[1069])).
% 0.50/0.73 tff(1071,plain,
% 0.50/0.73 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.50/0.73 inference(transitivity,[status(thm)],[1070, 1068])).
% 0.50/0.73 tff(1072,plain,
% 0.50/0.73 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(1073,plain,
% 0.57/0.73 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.57/0.73 tff(1074,plain,
% 0.57/0.73 (~big_p(sk1(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1073, 1046, 1042, 1057, 1067, 1047])).
% 0.57/0.73 tff(1075,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[383, 64, 9, 5, 377, 1074])).
% 0.57/0.73 tff(1076,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | (~big_p(sk7)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(1077,plain,
% 0.57/0.73 (big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1076, 5, 1046, 1042])).
% 0.57/0.73 tff(1078,plain,
% 0.57/0.73 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1063, 1046, 1042, 1057, 1077])).
% 0.57/0.73 tff(1079,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1078, 1045, 133])).
% 0.57/0.73 tff(1080,plain,(big_r(sk2(sk9), sk1(sk9)) | (~big_p(sk7)) | big_r(sk7, sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(1081,plain,
% 0.57/0.73 (big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1080, 5, 1042, 1043])).
% 0.57/0.73 tff(1082,plain,
% 0.57/0.73 (big_r(sk9, sk2(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1066, 1043, 5, 1042])).
% 0.57/0.73 tff(1083,plain,
% 0.57/0.73 (~big_p(sk1(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1073, 1043, 1042, 1057, 1082, 1081])).
% 0.57/0.73 tff(1084,plain,
% 0.57/0.73 (big_r(sk9, sk4(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[354, 162, 9, 5, 1083])).
% 0.57/0.73 tff(1085,plain,
% 0.57/0.73 (big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1076, 1043, 5, 1042])).
% 0.57/0.73 tff(1086,plain,
% 0.57/0.73 (~big_p(sk3(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1063, 1043, 1042, 1057, 1085, 1084])).
% 0.57/0.73 tff(1087,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[443, 19, 9, 5, 1083, 1086])).
% 0.57/0.73 tff(1088,plain,(big_p(sk9) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(1089,plain,
% 0.57/0.73 (big_p(sk9)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1088, 1042])).
% 0.57/0.73 tff(1090,plain,
% 0.57/0.73 (big_p(sk7)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[490, 448])).
% 0.57/0.73 tff(1091,plain,
% 0.57/0.73 (((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)) <=> ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1092,plain,
% 0.57/0.73 (((big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)) | (~big_p(sk9))) <=> ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1093,plain,
% 0.57/0.73 (((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) <=> (big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1094,plain,
% 0.57/0.73 ((((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)) | (~big_p(sk9)))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[1093])).
% 0.57/0.73 tff(1095,plain,
% 0.57/0.73 ((((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.57/0.73 inference(transitivity,[status(thm)],[1094, 1092])).
% 0.57/0.73 tff(1096,axiom,(((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_41')).
% 0.57/0.73 tff(1097,plain,
% 0.57/0.73 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.57/0.73 tff(1098,plain,
% 0.57/0.73 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1097, 1091])).
% 0.57/0.73 tff(1099,plain,
% 0.57/0.73 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1098, 1091])).
% 0.57/0.73 tff(1100,plain,
% 0.57/0.73 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1099, 1091])).
% 0.57/0.73 tff(1101,plain,
% 0.57/0.73 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1100, 1091])).
% 0.57/0.73 tff(1102,plain,
% 0.57/0.73 (~big_p(sk9)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1101, 1090, 448, 1042])).
% 0.57/0.73 tff(1103,plain,
% 0.57/0.73 (big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1080, 1090, 1042, 1102])).
% 0.57/0.73 tff(1104,plain,
% 0.57/0.73 (big_r(sk9, sk2(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1066, 1102, 1090, 1042])).
% 0.57/0.73 tff(1105,plain,
% 0.57/0.73 (~big_p(sk1(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1073, 1090, 1042, 1057, 1104, 1103])).
% 0.57/0.73 tff(1106,plain,
% 0.57/0.73 (big_p(sk3(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[443, 19, 9, 1102, 1105])).
% 0.57/0.73 tff(1107,plain,
% 0.57/0.73 (big_r(sk9, sk4(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[354, 162, 9, 1102, 1105])).
% 0.57/0.73 tff(1108,plain,
% 0.57/0.73 (big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1076, 1102, 1090, 1042])).
% 0.57/0.73 tff(1109,plain,
% 0.57/0.73 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1063, 1090, 1042, 1057, 1108])).
% 0.57/0.73 tff(1110,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1109, 1107, 1106])).
% 0.57/0.73 tff(1111,plain,(big_r(sk9, sk10) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(1112,plain,
% 0.57/0.73 (big_r(sk9, sk10)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1111, 1042])).
% 0.57/0.73 tff(1113,plain,
% 0.57/0.73 (big_p(sk7)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[1037, 1112, 1089])).
% 0.57/0.73 tff(1114,plain,
% 0.57/0.73 ((big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))) <=> (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1115,plain,
% 0.57/0.73 (((big_p(sk10) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1116,plain,
% 0.57/0.73 (((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) <=> (big_p(sk10) | big_r(sk7, sk8) | (~big_p(sk7)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(1117,plain,
% 0.57/0.73 ((((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((big_p(sk10) | big_r(sk7, sk8) | (~big_p(sk7))) | (~big_p(sk9)))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[1116])).
% 0.57/0.73 tff(1118,plain,
% 0.57/0.73 ((((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[1117, 1115])).
% 0.57/0.73 tff(1119,axiom,(((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_40')).
% 0.57/0.73 tff(1120,plain,
% 0.57/0.73 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.57/0.73 tff(1121,plain,
% 0.57/0.73 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1120, 1114])).
% 0.57/0.73 tff(1122,plain,
% 0.57/0.73 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[1121, 1114])).
% 0.57/0.74 tff(1123,plain,
% 0.57/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1122, 1114])).
% 0.57/0.74 tff(1124,plain,
% 0.57/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1123, 1114])).
% 0.57/0.74 tff(1125,plain,
% 0.57/0.74 (big_p(sk10)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1124, 1113, 1089, 1042])).
% 0.57/0.74 tff(1126,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[846, 840, 9, 1112])).
% 0.57/0.74 tff(1127,plain,
% 0.57/0.74 (big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1126, 830, 1125])).
% 0.57/0.74 tff(1128,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[883, 877, 9, 1112])).
% 0.57/0.74 tff(1129,plain,
% 0.57/0.74 (big_r(sk9, sk2(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1128, 830, 1125])).
% 0.57/0.74 tff(1130,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[924, 918, 9, 1112])).
% 0.57/0.74 tff(1131,plain,
% 0.57/0.74 (big_p(sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1130, 91, 1125])).
% 0.57/0.74 tff(1132,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[865, 859, 9, 1112])).
% 0.57/0.74 tff(1133,plain,
% 0.57/0.74 (big_r(sk9, sk6(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1132, 91, 1125])).
% 0.57/0.74 tff(1134,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[944, 938, 9, 1112])).
% 0.57/0.74 tff(1135,plain,
% 0.57/0.74 (big_r(sk6(sk9), sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1134, 91, 1125])).
% 0.57/0.74 tff(1136,plain,
% 0.57/0.74 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1137,plain,
% 0.57/0.74 (((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9)))) <=> (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1138,plain,
% 0.57/0.74 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | (big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[1137])).
% 0.57/0.74 tff(1139,plain,
% 0.57/0.74 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))) <=> ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.57/0.74 inference(transitivity,[status(thm)],[1138, 1136])).
% 0.57/0.74 tff(1140,plain,
% 0.57/0.74 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(1141,plain,
% 0.57/0.74 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.57/0.74 tff(1142,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1141, 1113, 1042, 1057, 1135, 1133, 1131])).
% 0.57/0.74 tff(1143,plain,(big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1144,plain,
% 0.57/0.74 (big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1143, 1042])).
% 0.57/0.74 tff(1145,plain,
% 0.57/0.74 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1073, 1113, 1042, 1057, 1144])).
% 0.57/0.74 tff(1146,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1145, 1129, 1127])).
% 0.57/0.74 tff(1147,plain,(big_r(sk9, sk6(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1148,plain,
% 0.57/0.74 (big_r(sk9, sk6(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1147, 1042])).
% 0.57/0.74 tff(1149,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[966, 960, 9, 1112])).
% 0.57/0.74 tff(1150,plain,
% 0.57/0.74 (big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1149, 950, 1125])).
% 0.57/0.74 tff(1151,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[984, 978, 9, 1112])).
% 0.57/0.74 tff(1152,plain,
% 0.57/0.74 (big_r(sk9, sk2(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1151, 950, 1125])).
% 0.57/0.74 tff(1153,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1145, 1152, 1150])).
% 0.57/0.74 tff(1154,plain,(big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1155,plain,
% 0.57/0.74 (big_r(sk6(sk9), sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1154, 1042])).
% 0.57/0.74 tff(1156,plain,
% 0.57/0.74 ((~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1141, 1113, 1042, 1057, 1155])).
% 0.57/0.74 tff(1157,plain,
% 0.57/0.74 (~big_p(sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1156, 1148])).
% 0.57/0.74 tff(1158,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1014, 1008, 9, 1112])).
% 0.57/0.74 tff(1159,plain,
% 0.57/0.74 (big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1158, 1157, 1125])).
% 0.57/0.74 tff(1160,plain,
% 0.57/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1032, 1026, 9, 1112])).
% 0.57/0.74 tff(1161,plain,
% 0.57/0.74 (big_r(sk9, sk2(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1160, 1157, 1125])).
% 0.57/0.74 tff(1162,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1145, 1161, 1159])).
% 0.57/0.74 tff(1163,plain,(big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1164,plain,
% 0.57/0.74 (big_r(sk9, sk2(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[321, 377])).
% 0.57/0.74 tff(1165,plain,
% 0.57/0.74 (^[F4: $i, E4: $i] : refl((big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4))) <=> (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(1166,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4))) <=> ![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1165])).
% 0.57/0.74 tff(1167,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4))) <=> ![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1168,plain,
% 0.57/0.74 (^[F4: $i, E4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) <=> (big_p(sk8) | (~big_p(E4)) | (~big_p(sk7)))), ((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) <=> ((big_p(sk8) | (~big_p(E4)) | (~big_p(sk7))) | (~big_r(F4, E4))))), rewrite(((big_p(sk8) | (~big_p(E4)) | (~big_p(sk7))) | (~big_r(F4, E4))) <=> (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)))), ((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) <=> (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7))))), (((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) | (~big_r(sk9, F4))) <=> ((big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7))) | (~big_r(sk9, F4))))), rewrite(((big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7))) | (~big_r(sk9, F4))) <=> (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))), (((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) | (~big_r(sk9, F4))) <=> (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(1169,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : ((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) | (~big_r(sk9, F4))) <=> ![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1168])).
% 0.57/0.74 tff(1170,axiom,(![F4: $i, E4: $i] : ((((big_p(sk8) | (~big_p(E4))) | (~big_p(sk7))) | (~big_r(F4, E4))) | (~big_r(sk9, F4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_42')).
% 0.57/0.74 tff(1171,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 0.57/0.74 tff(1172,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1171, 1167])).
% 0.57/0.74 tff(1173,plain,(
% 0.57/0.74 ![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[1172])).
% 0.57/0.74 tff(1174,plain,
% 0.57/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1173, 1166])).
% 0.57/0.74 tff(1175,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1176,plain,
% 0.57/0.74 ((big_p(sk8) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9)))) <=> (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1177,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[1176])).
% 0.57/0.74 tff(1178,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9))))),
% 0.57/0.74 inference(transitivity,[status(thm)],[1177, 1175])).
% 0.57/0.74 tff(1179,plain,
% 0.57/0.74 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(1180,plain,
% 0.57/0.74 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 0.57/0.74 tff(1181,plain,
% 0.57/0.74 (~big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1180, 2, 1039, 1174, 1164, 1047])).
% 0.57/0.74 tff(1182,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[383, 64, 9, 5, 377, 1181])).
% 0.57/0.74 tff(1183,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1184,plain,
% 0.57/0.74 (big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1183, 2, 5])).
% 0.57/0.74 tff(1185,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1186,plain,
% 0.57/0.74 ((big_p(sk8) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9)))) <=> (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1187,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[1186])).
% 0.57/0.74 tff(1188,plain,
% 0.57/0.74 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))))),
% 0.57/0.74 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.57/0.74 tff(1189,plain,
% 0.57/0.74 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk4(sk9))))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(1190,plain,
% 0.57/0.74 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.57/0.74 tff(1191,plain,
% 0.57/0.74 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1190, 2, 1039, 1174, 1184])).
% 0.57/0.74 tff(1192,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1191, 330, 53])).
% 0.57/0.74 tff(1193,plain,(big_r(sk9, sk2(sk9)) | big_p(sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1194,plain,
% 0.57/0.74 (big_r(sk9, sk2(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1193, 2, 5])).
% 0.57/0.74 tff(1195,plain,
% 0.57/0.74 (~big_p(sk3(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1191, 133])).
% 0.57/0.74 tff(1196,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[114, 101, 9, 5, 91, 1195])).
% 0.57/0.74 tff(1197,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1198,plain,
% 0.57/0.74 (big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1197, 2, 5])).
% 0.57/0.74 tff(1199,plain,
% 0.57/0.74 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1180, 2, 1039, 1174, 1198])).
% 0.57/0.74 tff(1200,plain,
% 0.57/0.74 (~big_p(sk1(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1199, 1194])).
% 0.57/0.74 tff(1201,plain,
% 0.57/0.74 (big_p(sk3(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[444, 1200])).
% 0.57/0.74 tff(1202,plain,
% 0.57/0.74 (big_r(sk9, sk4(sk9))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[355, 1200])).
% 0.57/0.74 tff(1203,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1191, 1202, 1201])).
% 0.57/0.74 tff(1204,plain,(big_p(sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1205,plain,
% 0.57/0.74 (big_p(sk8)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1204, 5])).
% 0.57/0.74 tff(1206,plain,
% 0.57/0.74 (^[M1: $i, L1: $i, K1: $i] : refl(((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(1207,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> ![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1206])).
% 0.57/0.74 tff(1208,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> ![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1209,plain,
% 0.57/0.74 (^[M1: $i, L1: $i, K1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) <=> (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1))), ((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) <=> ((big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1)) | (~big_p(M1))))), rewrite(((big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1)) | (~big_p(M1))) <=> (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1)))), ((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) <=> (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))))), (((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) <=> ((big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))) | (~big_p(a))))), rewrite(((big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1)))), (((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))))), ((((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) | (~big_r(L1, M1))) <=> (((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))) | (~big_r(L1, M1))))), rewrite((((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_p(M1))) | (~big_r(L1, M1))) <=> ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))), ((((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) | (~big_r(L1, M1))) <=> ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(1210,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : (((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) | (~big_r(L1, M1))) <=> ![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[1209])).
% 0.57/0.74 tff(1211,axiom,(![M1: $i, L1: $i, K1: $i] : (((((big_p(K1) | big_p(sk1(L1))) | big_p(sk3(K1))) | (~big_p(M1))) | (~big_p(a))) | (~big_r(L1, M1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_16')).
% 0.57/0.74 tff(1212,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.57/0.74 tff(1213,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1212, 1208])).
% 0.57/0.74 tff(1214,plain,(
% 0.57/0.74 ![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[1213])).
% 0.57/0.74 tff(1215,plain,
% 0.57/0.74 (![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1214, 1207])).
% 0.57/0.74 tff(1216,plain,
% 0.57/0.74 (((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))) <=> ((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1217,plain,
% 0.57/0.74 (((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1218,plain,
% 0.57/0.75 (((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1217])).
% 0.57/0.75 tff(1219,plain,
% 0.57/0.75 (((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1218, 1216])).
% 0.57/0.75 tff(1220,plain,
% 0.57/0.75 ((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | ((~big_p(a)) | big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1221,plain,
% 0.57/0.75 ((~![M1: $i, L1: $i, K1: $i] : ((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 0.57/0.75 tff(1222,plain,
% 0.57/0.75 (big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1221, 1215, 9, 1205, 5, 1163])).
% 0.57/0.75 tff(1223,plain,
% 0.57/0.75 (big_p(sk1(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1222, 1040])).
% 0.57/0.75 tff(1224,plain,
% 0.57/0.75 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1225,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1226,plain,
% 0.57/0.75 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1225])).
% 0.57/0.75 tff(1227,plain,
% 0.57/0.75 (((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.57/0.75 tff(1228,plain,
% 0.57/0.75 ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1229,plain,
% 0.57/0.75 ((~![M2: $i, L2: $i, N2: $i] : ((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.57/0.75 tff(1230,plain,
% 0.57/0.75 ((~big_p(sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1229, 714, 9, 5, 1163])).
% 0.57/0.75 tff(1231,plain,
% 0.57/0.75 (big_p(sk5(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1230, 91, 1205])).
% 0.57/0.75 tff(1232,plain,
% 0.57/0.75 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1233,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1234,plain,
% 0.57/0.75 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1233])).
% 0.57/0.75 tff(1235,plain,
% 0.57/0.75 (((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1234, 1232])).
% 0.57/0.75 tff(1236,plain,
% 0.57/0.75 ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1237,plain,
% 0.57/0.75 ((~![O2: $i, P2: $i, Q2: $i] : ((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.57/0.75 tff(1238,plain,
% 0.57/0.75 ((~big_p(sk8)) | big_r(sk7, sk6(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1237, 732, 9, 5, 1163])).
% 0.57/0.75 tff(1239,plain,
% 0.57/0.75 (big_r(sk7, sk6(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1238, 91, 1205])).
% 0.57/0.75 tff(1240,plain,
% 0.57/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1241,plain,
% 0.57/0.75 ((big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1242,plain,
% 0.57/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1241])).
% 0.57/0.75 tff(1243,plain,
% 0.57/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1242, 1240])).
% 0.57/0.75 tff(1244,plain,
% 0.57/0.75 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1245,plain,
% 0.57/0.75 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | (~big_p(a)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.57/0.75 tff(1246,plain,
% 0.57/0.75 (big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1245, 750, 9, 1205, 5, 1163])).
% 0.57/0.75 tff(1247,plain,
% 0.57/0.75 (big_r(sk6(sk7), sk5(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1246, 91])).
% 0.57/0.75 tff(1248,plain,
% 0.57/0.75 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1249,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1250,plain,
% 0.57/0.75 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1249])).
% 0.57/0.75 tff(1251,plain,
% 0.57/0.75 (((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.57/0.75 tff(1252,plain,
% 0.57/0.75 ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1253,plain,
% 0.57/0.75 ((~![R1: $i, S1: $i, Q1: $i] : ((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.57/0.75 tff(1254,plain,
% 0.57/0.75 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk9, sk4(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1253, 658, 9, 5, 1163])).
% 0.57/0.75 tff(1255,plain,
% 0.57/0.75 (big_p(sk1(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1254, 348, 1205])).
% 0.57/0.75 tff(1256,plain,
% 0.57/0.75 (big_r(sk2(sk9), sk1(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[132, 348])).
% 0.57/0.75 tff(1257,plain,
% 0.57/0.75 (((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1258,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1259,plain,
% 0.57/0.75 (((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)))) <=> ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1258])).
% 0.57/0.75 tff(1260,plain,
% 0.57/0.75 (((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)))) <=> ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.57/0.75 tff(1261,plain,
% 0.57/0.75 ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1262,plain,
% 0.57/0.75 ((~![W: $i, V: $i, X: $i] : ((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.57/0.75 tff(1263,plain,
% 0.57/0.75 ((~big_p(sk8)) | big_p(sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1262, 777, 9, 5, 1163])).
% 0.57/0.75 tff(1264,plain,
% 0.57/0.75 (big_p(sk5(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1263, 3, 1205])).
% 0.57/0.75 tff(1265,plain,
% 0.57/0.75 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1266,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1267,plain,
% 0.57/0.75 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1266])).
% 0.57/0.75 tff(1268,plain,
% 0.57/0.75 (((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1267, 1265])).
% 0.57/0.75 tff(1269,plain,
% 0.57/0.75 ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1270,plain,
% 0.57/0.75 ((~![Z: $i, A1: $i, Y: $i] : ((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.57/0.75 tff(1271,plain,
% 0.57/0.75 ((~big_p(sk8)) | big_r(sk7, sk6(sk7)) | big_r(sk9, sk2(sk9))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1270, 792, 9, 5, 1163])).
% 0.57/0.75 tff(1272,plain,
% 0.57/0.75 (big_r(sk7, sk6(sk7))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1271, 3, 1205])).
% 0.57/0.75 tff(1273,plain,
% 0.57/0.75 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1274,plain,
% 0.57/0.75 (((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1275,plain,
% 0.57/0.75 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1274])).
% 0.57/0.76 tff(1276,plain,
% 0.57/0.76 (((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1275, 1273])).
% 0.57/0.76 tff(1277,plain,
% 0.57/0.76 ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | ((~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1278,plain,
% 0.57/0.76 ((~![B1: $i, D1: $i, C1: $i] : ((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.57/0.76 tff(1279,plain,
% 0.57/0.76 ((~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1278, 810, 9, 5, 1163])).
% 0.57/0.76 tff(1280,plain,
% 0.57/0.76 (big_r(sk6(sk7), sk5(sk7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1279, 3, 1205])).
% 0.57/0.76 tff(1281,plain,
% 0.57/0.76 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1282,plain,
% 0.57/0.76 (((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1283,plain,
% 0.57/0.76 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1282])).
% 0.57/0.76 tff(1284,plain,
% 0.57/0.76 (((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1283, 1281])).
% 0.57/0.76 tff(1285,plain,
% 0.57/0.76 ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1286,plain,
% 0.57/0.76 ((~![D2: $i, E2: $i, C2: $i] : ((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk9) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 0.57/0.76 tff(1287,plain,
% 0.57/0.76 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1286, 600, 9, 5, 1163])).
% 0.57/0.76 tff(1288,plain,
% 0.57/0.76 (big_p(sk1(sk7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1287, 377, 1205])).
% 0.57/0.76 tff(1289,plain,
% 0.57/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1290,plain,
% 0.57/0.76 ((big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1291,plain,
% 0.57/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1290])).
% 0.57/0.76 tff(1292,plain,
% 0.57/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1291, 1289])).
% 0.57/0.76 tff(1293,plain,
% 0.57/0.76 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1294,plain,
% 0.57/0.76 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | (~big_p(a)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.57/0.76 tff(1295,plain,
% 0.57/0.76 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1294, 618, 9, 5, 1163])).
% 0.57/0.76 tff(1296,plain,
% 0.57/0.76 (big_r(sk2(sk7), sk1(sk7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1295, 377, 1205])).
% 0.57/0.76 tff(1297,plain,
% 0.57/0.76 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1298,plain,
% 0.57/0.76 (((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1299,plain,
% 0.57/0.76 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1298])).
% 0.57/0.76 tff(1300,plain,
% 0.57/0.76 (((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)))) <=> ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1299, 1297])).
% 0.57/0.76 tff(1301,plain,
% 0.57/0.76 ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1302,plain,
% 0.57/0.76 ((~![G2: $i, H2: $i, F2: $i] : ((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 0.57/0.76 tff(1303,plain,
% 0.57/0.76 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1302, 636, 9, 5, 1163])).
% 0.57/0.76 tff(1304,plain,
% 0.57/0.76 (big_r(sk7, sk2(sk7))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1303, 377, 1205])).
% 0.57/0.76 tff(1305,plain,
% 0.57/0.76 (~big_p(sk1(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[280, 250, 1304, 1296, 1164, 1047, 1288])).
% 0.57/0.76 tff(1306,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[383, 64, 9, 5, 377, 1305])).
% 0.57/0.76 tff(1307,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(1308,plain,
% 0.57/0.76 (big_r(sk4(sk9), sk3(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1307, 5])).
% 0.57/0.76 tff(1309,plain,
% 0.57/0.76 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1310,plain,
% 0.57/0.76 (((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk4(sk9)))) <=> ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1311,plain,
% 0.57/0.76 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1310])).
% 0.57/0.76 tff(1312,plain,
% 0.57/0.76 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk4(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1311, 1309])).
% 0.57/0.76 tff(1313,plain,
% 0.57/0.76 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk4(sk9))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1314,plain,
% 0.57/0.76 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 0.57/0.76 tff(1315,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1314, 250, 1308, 53, 1280, 1272, 1264, 330])).
% 0.57/0.76 tff(1316,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(1317,plain,
% 0.57/0.76 (big_r(sk9, sk2(sk9))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1316, 5])).
% 0.57/0.76 tff(1318,plain,
% 0.57/0.76 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1319,plain,
% 0.60/0.76 (((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1320,plain,
% 0.60/0.76 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1319])).
% 0.60/0.76 tff(1321,plain,
% 0.60/0.76 (((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1320, 1318])).
% 0.60/0.76 tff(1322,plain,
% 0.60/0.76 ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk9, sk4(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1323,plain,
% 0.60/0.76 ((~![A2: $i, B2: $i, Z1: $i] : ((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 0.60/0.76 tff(1324,plain,
% 0.60/0.76 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk4(sk9))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1323, 678, 9, 5, 1163])).
% 0.60/0.76 tff(1325,plain,
% 0.60/0.76 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1324, 348, 1205])).
% 0.60/0.76 tff(1326,plain,
% 0.60/0.76 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1327,plain,
% 0.60/0.76 (((~big_p(a)) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1328,plain,
% 0.60/0.76 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1327])).
% 0.60/0.76 tff(1329,plain,
% 0.60/0.76 (((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1328, 1326])).
% 0.60/0.76 tff(1330,plain,
% 0.60/0.76 ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | ((~big_p(a)) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1331,plain,
% 0.60/0.76 ((~![V1: $i, T1: $i, U1: $i] : ((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.60/0.77 tff(1332,plain,
% 0.60/0.77 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk9, sk4(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1331, 696, 9, 5, 1163])).
% 0.60/0.77 tff(1333,plain,
% 0.60/0.77 (big_r(sk7, sk2(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1332, 348, 1205])).
% 0.60/0.77 tff(1334,plain,
% 0.60/0.77 (~big_p(sk1(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[280, 250, 1333, 1325, 1317, 1256, 1255])).
% 0.60/0.77 tff(1335,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[354, 162, 9, 5, 348, 1334])).
% 0.60/0.77 tff(1336,plain,(big_r(sk9, sk4(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1337,plain,
% 0.60/0.77 (big_r(sk9, sk4(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1336, 5])).
% 0.60/0.77 tff(1338,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1314, 250, 1308, 1337, 1247, 1239, 1231, 1045])).
% 0.60/0.77 tff(1339,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1340,plain,
% 0.60/0.77 (big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1339, 5])).
% 0.60/0.77 tff(1341,plain,
% 0.60/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1342,plain,
% 0.60/0.77 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1343,plain,
% 0.60/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1342])).
% 0.60/0.77 tff(1344,plain,
% 0.60/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1343, 1341])).
% 0.60/0.77 tff(1345,plain,
% 0.60/0.77 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | (~big_p(a)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1346,plain,
% 0.60/0.77 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | (~big_p(a)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 0.60/0.77 tff(1347,plain,
% 0.60/0.77 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1346, 900, 9, 1205, 5, 1163])).
% 0.60/0.77 tff(1348,plain,
% 0.60/0.77 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1347, 1040])).
% 0.60/0.77 tff(1349,plain,
% 0.60/0.77 (^[N1: $i, O1: $i, P1: $i] : refl(((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1350,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> ![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1349])).
% 0.60/0.77 tff(1351,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> ![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1352,plain,
% 0.60/0.77 (^[N1: $i, O1: $i, P1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) <=> (big_r(O1, sk2(O1)) | big_p(N1) | big_p(sk3(N1)))), ((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) <=> ((big_r(O1, sk2(O1)) | big_p(N1) | big_p(sk3(N1))) | (~big_p(P1))))), rewrite(((big_r(O1, sk2(O1)) | big_p(N1) | big_p(sk3(N1))) | (~big_p(P1))) <=> (big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1)))), ((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) <=> (big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))))), (((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) <=> ((big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))) | (~big_p(a))))), rewrite(((big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1)))), (((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) <=> ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))))), ((((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) | (~big_r(O1, P1))) <=> (((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))) | (~big_r(O1, P1))))), rewrite((((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_p(P1)) | big_p(sk3(N1))) | (~big_r(O1, P1))) <=> ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))), ((((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) | (~big_r(O1, P1))) <=> ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1353,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : (((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) | (~big_r(O1, P1))) <=> ![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1352])).
% 0.60/0.77 tff(1354,axiom,(![N1: $i, O1: $i, P1: $i] : (((((big_p(N1) | big_p(sk3(N1))) | big_r(O1, sk2(O1))) | (~big_p(P1))) | (~big_p(a))) | (~big_r(O1, P1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_17')).
% 0.60/0.77 tff(1355,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 0.60/0.77 tff(1356,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1355, 1351])).
% 0.60/0.77 tff(1357,plain,(
% 0.60/0.77 ![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[1356])).
% 0.60/0.77 tff(1358,plain,
% 0.60/0.77 (![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1357, 1350])).
% 0.60/0.77 tff(1359,plain,
% 0.60/0.77 (((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))) <=> ((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1360,plain,
% 0.60/0.77 (((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9))) <=> (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1361,plain,
% 0.60/0.77 (((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9)))) <=> ((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1360])).
% 0.60/0.77 tff(1362,plain,
% 0.60/0.77 (((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9)))) <=> ((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1361, 1359])).
% 0.60/0.77 tff(1363,plain,
% 0.60/0.77 ((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1364,plain,
% 0.60/0.77 ((~![N1: $i, O1: $i, P1: $i] : ((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.60/0.77 tff(1365,plain,
% 0.60/0.77 (big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1364, 1358, 9, 1205, 5, 1163])).
% 0.60/0.77 tff(1366,plain,
% 0.60/0.77 (big_r(sk7, sk2(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1365, 1040])).
% 0.60/0.77 tff(1367,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[280, 250, 1366, 1348, 1317, 1340, 1223, 1041])).
% 0.60/0.77 tff(1368,plain,(big_p(sk3(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1369,plain,
% 0.60/0.77 (big_p(sk3(sk9))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1368, 5])).
% 0.60/0.77 tff(1370,assumption,(big_p(sk3(sk9))), introduced(assumption)).
% 0.60/0.77 tff(1371,assumption,(big_p(sk8)), introduced(assumption)).
% 0.60/0.77 tff(1372,plain,
% 0.60/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1373,plain,
% 0.60/0.77 (((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7))) <=> ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1374,plain,
% 0.60/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1373])).
% 0.60/0.77 tff(1375,plain,
% 0.60/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1374, 1372])).
% 0.60/0.77 tff(1376,plain,
% 0.60/0.77 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1377,plain,
% 0.60/0.77 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.60/0.77 tff(1378,plain,
% 0.60/0.77 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1377, 1008, 9, 1163])).
% 0.60/0.77 tff(1379,plain,
% 0.60/0.77 (big_p(sk5(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1378, 6, 1371])).
% 0.60/0.77 tff(1380,plain,
% 0.60/0.77 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1381,plain,
% 0.60/0.77 (((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1382,plain,
% 0.60/0.77 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1381])).
% 0.60/0.77 tff(1383,plain,
% 0.60/0.77 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1382, 1380])).
% 0.60/0.77 tff(1384,plain,
% 0.60/0.77 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1385,plain,
% 0.60/0.77 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.60/0.77 tff(1386,plain,
% 0.60/0.77 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1385, 840, 9, 1163])).
% 0.60/0.77 tff(1387,plain,
% 0.60/0.77 (big_r(sk7, sk6(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1386, 6, 1371])).
% 0.60/0.77 tff(1388,plain,
% 0.60/0.77 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1389,plain,
% 0.60/0.77 (((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7))) <=> ((~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1390,plain,
% 0.60/0.77 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1389])).
% 0.60/0.77 tff(1391,plain,
% 0.60/0.77 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1390, 1388])).
% 0.60/0.77 tff(1392,plain,
% 0.60/0.77 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1393,plain,
% 0.60/0.77 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.60/0.77 tff(1394,plain,
% 0.60/0.77 ((~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1393, 960, 9, 1163])).
% 0.60/0.78 tff(1395,plain,
% 0.60/0.78 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1394, 6, 1371])).
% 0.60/0.78 tff(1396,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1314, 250, 340, 339, 1395, 1387, 1379, 1370])).
% 0.60/0.78 tff(1397,plain,(big_p(sk1(sk7)) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk8))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1398,plain,
% 0.60/0.78 (big_p(sk1(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1397, 340, 339, 1370, 1371])).
% 0.60/0.78 tff(1399,plain,
% 0.60/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1400,plain,
% 0.60/0.78 (((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1401,plain,
% 0.60/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1400])).
% 0.60/0.78 tff(1402,plain,
% 0.60/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1401, 1399])).
% 0.60/0.78 tff(1403,plain,
% 0.60/0.78 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1404,plain,
% 0.60/0.78 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.60/0.78 tff(1405,plain,
% 0.60/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1404, 918, 9, 1163])).
% 0.60/0.78 tff(1406,plain,
% 0.60/0.78 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1405, 1, 1371])).
% 0.60/0.78 tff(1407,plain,
% 0.60/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1408,plain,
% 0.60/0.78 (((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1409,plain,
% 0.60/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1408])).
% 0.60/0.78 tff(1410,plain,
% 0.60/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1409, 1407])).
% 0.60/0.78 tff(1411,plain,
% 0.60/0.78 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1412,plain,
% 0.60/0.78 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 0.60/0.78 tff(1413,plain,
% 0.60/0.78 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1412, 1026, 9, 1163])).
% 0.60/0.78 tff(1414,plain,
% 0.60/0.78 (big_r(sk7, sk2(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1413, 1, 1371])).
% 0.60/0.78 tff(1415,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[435, 250, 1414, 1406, 340, 339, 1398, 1370])).
% 0.60/0.78 tff(1416,plain,(big_p(sk5(sk7)) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk8))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1417,plain,
% 0.60/0.78 (big_p(sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1416, 1308, 1337, 1369, 1205])).
% 0.60/0.78 tff(1418,plain,
% 0.60/0.78 (big_p(sk1(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1397, 1308, 1337, 1369, 1205])).
% 0.60/0.78 tff(1419,plain,
% 0.60/0.78 (big_p(sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1416, 340, 339, 1370, 1371])).
% 0.60/0.78 tff(1420,plain,
% 0.60/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1421,plain,
% 0.60/0.78 (((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1422,plain,
% 0.60/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1421])).
% 0.60/0.78 tff(1423,plain,
% 0.60/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1422, 1420])).
% 0.60/0.78 tff(1424,plain,
% 0.60/0.78 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1425,plain,
% 0.60/0.78 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.60/0.78 tff(1426,plain,
% 0.60/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1425, 859, 9, 1163])).
% 0.60/0.78 tff(1427,plain,
% 0.60/0.78 (big_r(sk7, sk6(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1426, 394, 1371])).
% 0.60/0.78 tff(1428,plain,
% 0.60/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1429,plain,
% 0.60/0.78 (((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1430,plain,
% 0.60/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1429])).
% 0.60/0.78 tff(1431,plain,
% 0.60/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.60/0.78 tff(1432,plain,
% 0.60/0.78 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1433,plain,
% 0.60/0.78 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.60/0.78 tff(1434,plain,
% 0.60/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1433, 938, 9, 1163])).
% 0.60/0.78 tff(1435,plain,
% 0.60/0.78 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1434, 394, 1371])).
% 0.60/0.78 tff(1436,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1314, 250, 340, 339, 1435, 1427, 1419, 1370])).
% 0.60/0.78 tff(1437,plain,(big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_p(sk3(sk9))) | (~big_p(sk8))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1438,plain,
% 0.60/0.78 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1437, 1308, 1337, 1369, 1205])).
% 0.60/0.78 tff(1439,plain,
% 0.60/0.78 (~big_r(sk7, sk2(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[435, 250, 1438, 1308, 1337, 1418, 1369])).
% 0.60/0.78 tff(1440,plain,
% 0.60/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1441,plain,
% 0.60/0.78 (((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1442,plain,
% 0.60/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1441])).
% 0.60/0.78 tff(1443,plain,
% 0.60/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1442, 1440])).
% 0.60/0.78 tff(1444,plain,
% 0.60/0.78 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1445,plain,
% 0.60/0.78 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.60/0.78 tff(1446,plain,
% 0.60/0.78 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1445, 877, 9, 1163])).
% 0.60/0.78 tff(1447,plain,
% 0.60/0.78 (big_r(sk7, sk6(sk7))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1446, 1439, 1205])).
% 0.60/0.78 tff(1448,plain,
% 0.60/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1449,plain,
% 0.60/0.78 (((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1450,plain,
% 0.60/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1449])).
% 0.60/0.78 tff(1451,plain,
% 0.60/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1450, 1448])).
% 0.60/0.78 tff(1452,plain,
% 0.60/0.78 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1453,plain,
% 0.60/0.78 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 0.60/0.79 tff(1454,plain,
% 0.60/0.79 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1453, 978, 9, 1163])).
% 0.60/0.79 tff(1455,plain,
% 0.60/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1454, 1439, 1205])).
% 0.60/0.79 tff(1456,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1314, 250, 1308, 1337, 1455, 1447, 1417, 1369])).
% 0.60/0.79 tff(1457,plain,(big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1458,plain,
% 0.60/0.79 ((big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)) <=> (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1459,plain,
% 0.60/0.79 (((big_p(sk8) | (~big_p(sk7)) | big_r(sk9, sk10)) | (~big_p(sk9))) <=> (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1460,plain,
% 0.60/0.79 (((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) <=> (big_p(sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1461,plain,
% 0.60/0.79 ((((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((big_p(sk8) | (~big_p(sk7)) | big_r(sk9, sk10)) | (~big_p(sk9)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1460])).
% 0.60/0.79 tff(1462,plain,
% 0.60/0.79 ((((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1461, 1459])).
% 0.60/0.79 tff(1463,axiom,(((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_39')).
% 0.60/0.79 tff(1464,plain,
% 0.60/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 0.60/0.79 tff(1465,plain,
% 0.60/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1464, 1458])).
% 0.60/0.79 tff(1466,plain,
% 0.60/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1465, 1458])).
% 0.60/0.79 tff(1467,plain,
% 0.60/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1466, 1458])).
% 0.60/0.79 tff(1468,plain,
% 0.60/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1467, 1458])).
% 0.60/0.79 tff(1469,plain,
% 0.60/0.79 (big_r(sk9, sk10)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1468, 2, 1457, 1039])).
% 0.60/0.79 tff(1470,plain,
% 0.60/0.79 ((big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1471,plain,
% 0.60/0.79 (((big_p(sk8) | big_p(sk10) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1472,plain,
% 0.60/0.79 (((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk7)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1473,plain,
% 0.60/0.79 ((((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((big_p(sk8) | big_p(sk10) | (~big_p(sk7))) | (~big_p(sk9)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1472])).
% 0.60/0.79 tff(1474,plain,
% 0.60/0.79 ((((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1473, 1471])).
% 0.60/0.79 tff(1475,axiom,(((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel38_38')).
% 0.60/0.79 tff(1476,plain,
% 0.60/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 0.60/0.79 tff(1477,plain,
% 0.60/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1476, 1470])).
% 0.60/0.79 tff(1478,plain,
% 0.60/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1477, 1470])).
% 0.60/0.79 tff(1479,plain,
% 0.60/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1478, 1470])).
% 0.60/0.79 tff(1480,plain,
% 0.60/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1479, 1470])).
% 0.60/0.79 tff(1481,plain,
% 0.60/0.79 (big_p(sk10)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1480, 2, 1457, 1039])).
% 0.60/0.79 tff(1482,plain,
% 0.60/0.79 (big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1032, 1026, 9, 1481, 1469])).
% 0.60/0.79 tff(1483,plain,
% 0.60/0.79 (big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1482, 3])).
% 0.60/0.79 tff(1484,plain,
% 0.60/0.79 (big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[984, 978, 9, 1481, 1469])).
% 0.60/0.79 tff(1485,plain,
% 0.60/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1484, 3])).
% 0.60/0.79 tff(1486,plain,
% 0.60/0.79 (big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[883, 877, 9, 1481, 1469])).
% 0.60/0.79 tff(1487,plain,
% 0.60/0.79 (big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1486, 3])).
% 0.60/0.79 tff(1488,plain,
% 0.60/0.79 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1489,plain,
% 0.60/0.79 ((big_p(sk8) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9)))) <=> (big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1490,plain,
% 0.60/0.79 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1489])).
% 0.60/0.79 tff(1491,plain,
% 0.60/0.79 (((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))) <=> ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1490, 1488])).
% 0.60/0.79 tff(1492,plain,
% 0.60/0.79 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | (big_p(sk8) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_p(sk7)) | (~big_r(sk9, sk6(sk9))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1493,plain,
% 0.60/0.79 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.60/0.79 tff(1494,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1493, 2, 1039, 1174, 1487, 1485, 1483])).
% 0.60/0.79 tff(1495,plain,(big_r(sk9, sk2(sk9)) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1496,plain,
% 0.60/0.79 (big_r(sk9, sk2(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1495, 2])).
% 0.60/0.79 tff(1497,plain,
% 0.60/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[924, 918, 9, 1481, 1469])).
% 0.60/0.79 tff(1498,plain,
% 0.60/0.79 (big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1497, 91])).
% 0.60/0.79 tff(1499,plain,
% 0.60/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[944, 938, 9, 1481, 1469])).
% 0.60/0.79 tff(1500,plain,
% 0.60/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1499, 91])).
% 0.60/0.79 tff(1501,plain,
% 0.60/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[865, 859, 9, 1481, 1469])).
% 0.60/0.79 tff(1502,plain,
% 0.60/0.79 (big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1501, 91])).
% 0.60/0.79 tff(1503,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1493, 2, 1039, 1174, 1502, 1500, 1498])).
% 0.60/0.79 tff(1504,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1505,plain,
% 0.60/0.79 (big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1504, 2])).
% 0.60/0.79 tff(1506,plain,
% 0.60/0.79 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1180, 2, 1039, 1174, 1505])).
% 0.60/0.79 tff(1507,plain,
% 0.60/0.79 (~big_p(sk1(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1506, 1496])).
% 0.60/0.79 tff(1508,plain,
% 0.60/0.79 (big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1014, 1008, 9, 1481, 1469])).
% 0.60/0.79 tff(1509,plain,
% 0.60/0.79 (big_p(sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1508, 1507])).
% 0.60/0.79 tff(1510,plain,
% 0.60/0.79 (big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[966, 960, 9, 1481, 1469])).
% 0.60/0.79 tff(1511,plain,
% 0.60/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1510, 1507])).
% 0.60/0.79 tff(1512,plain,
% 0.60/0.79 (big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[846, 840, 9, 1481, 1469])).
% 0.60/0.79 tff(1513,plain,
% 0.60/0.79 (big_r(sk9, sk6(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1512, 1507])).
% 0.60/0.79 tff(1514,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1493, 2, 1039, 1174, 1513, 1511, 1509])).
% 0.60/0.79 tff(1515,plain,(big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1516,plain,
% 0.60/0.79 (big_p(sk1(sk7)) | big_p(sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1378, 1515])).
% 0.60/0.79 tff(1517,plain,
% 0.60/0.79 (big_p(sk1(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1516, 1])).
% 0.60/0.79 tff(1518,plain,
% 0.60/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1405, 1515])).
% 0.60/0.79 tff(1519,plain,
% 0.60/0.79 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1518, 1])).
% 0.60/0.79 tff(1520,plain,
% 0.60/0.79 (big_r(sk7, sk2(sk7)) | big_p(sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1413, 1515])).
% 0.60/0.79 tff(1521,plain,
% 0.60/0.79 (big_r(sk7, sk2(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1520, 1])).
% 0.60/0.79 tff(1522,plain,
% 0.60/0.79 (big_p(sk10)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[520, 1457, 504, 1521, 1519, 1517])).
% 0.60/0.79 tff(1523,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[467, 1457, 448, 461, 1521, 1519, 1517])).
% 0.60/0.79 tff(1524,plain,(big_p(sk5(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1525,plain,
% 0.60/0.79 (big_p(sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1524, 448])).
% 0.60/0.79 tff(1526,plain,
% 0.60/0.79 (big_p(sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1386, 1515])).
% 0.60/0.79 tff(1527,plain,
% 0.60/0.79 (big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1526, 6])).
% 0.60/0.79 tff(1528,plain,
% 0.60/0.79 (big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1394, 1515])).
% 0.60/0.79 tff(1529,plain,
% 0.60/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1528, 6])).
% 0.60/0.79 tff(1530,plain,
% 0.60/0.79 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1531,plain,
% 0.60/0.79 (((~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk6(sk7)))) <=> ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1532,plain,
% 0.60/0.79 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk6(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1531])).
% 0.60/0.79 tff(1533,plain,
% 0.60/0.79 (((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk6(sk7))))) <=> ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1532, 1530])).
% 0.60/0.79 tff(1534,plain,
% 0.60/0.79 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | ((~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | big_r(sk9, sk10) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1535,plain,
% 0.60/0.79 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.60/0.79 tff(1536,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1535, 1457, 448, 461, 1529, 1527, 1525])).
% 0.60/0.79 tff(1537,plain,(big_p(sk1(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1538,plain,
% 0.60/0.79 (big_p(sk1(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1537, 448])).
% 0.60/0.79 tff(1539,plain,
% 0.60/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1426, 1515])).
% 0.60/0.79 tff(1540,plain,
% 0.60/0.79 (big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1539, 394])).
% 0.60/0.79 tff(1541,plain,
% 0.60/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1434, 1515])).
% 0.60/0.79 tff(1542,plain,
% 0.60/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1541, 394])).
% 0.60/0.79 tff(1543,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1535, 1457, 448, 461, 1542, 1540, 1525])).
% 0.60/0.79 tff(1544,plain,(big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1545,plain,
% 0.60/0.79 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1544, 448])).
% 0.60/0.79 tff(1546,plain,
% 0.60/0.79 ((~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[467, 1457, 448, 461, 1545])).
% 0.60/0.79 tff(1547,plain,
% 0.60/0.79 (~big_r(sk7, sk2(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1546, 1538])).
% 0.60/0.79 tff(1548,plain,
% 0.60/0.79 (big_r(sk7, sk2(sk7)) | big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1446, 1515])).
% 0.60/0.79 tff(1549,plain,
% 0.60/0.79 (big_r(sk7, sk6(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1548, 1547])).
% 0.60/0.79 tff(1550,plain,
% 0.60/0.79 (big_r(sk7, sk2(sk7)) | big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1454, 1515])).
% 0.60/0.79 tff(1551,plain,
% 0.60/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1550, 1547])).
% 0.60/0.79 tff(1552,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1535, 1457, 448, 461, 1551, 1549, 1525])).
% 0.60/0.79 tff(1553,plain,(big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1554,plain,
% 0.60/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1555,plain,
% 0.60/0.79 (((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1556,plain,
% 0.60/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1555])).
% 0.60/0.79 tff(1557,plain,
% 0.60/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1556, 1554])).
% 0.60/0.79 tff(1558,plain,
% 0.60/0.79 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1559,plain,
% 0.60/0.79 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.60/0.79 tff(1560,plain,
% 0.60/0.79 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1559, 1008, 9, 1515, 1553, 1163])).
% 0.60/0.79 tff(1561,plain,
% 0.60/0.79 (big_p(sk1(sk9))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1560, 1522, 1])).
% 0.60/0.79 tff(1562,plain,
% 0.60/0.79 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1563,plain,
% 0.60/0.79 (((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1564,plain,
% 0.60/0.80 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1563])).
% 0.60/0.80 tff(1565,plain,
% 0.60/0.80 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1564, 1562])).
% 0.60/0.80 tff(1566,plain,
% 0.60/0.80 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1567,plain,
% 0.60/0.80 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 0.60/0.80 tff(1568,plain,
% 0.60/0.80 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1567, 918, 9, 1515, 1553, 1163])).
% 0.60/0.80 tff(1569,plain,
% 0.60/0.80 (big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1568, 1522, 1])).
% 0.60/0.80 tff(1570,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1571,plain,
% 0.60/0.80 (((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1572,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1571])).
% 0.60/0.80 tff(1573,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1572, 1570])).
% 0.60/0.80 tff(1574,plain,
% 0.60/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1575,plain,
% 0.60/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 0.60/0.80 tff(1576,plain,
% 0.60/0.80 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1575, 1026, 9, 1515, 1553, 1163])).
% 0.60/0.80 tff(1577,plain,
% 0.60/0.80 (big_r(sk9, sk2(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1576, 1522, 1])).
% 0.60/0.80 tff(1578,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[280, 250, 1521, 1519, 1577, 1569, 1517, 1561])).
% 0.60/0.80 tff(1579,plain,(big_p(sk5(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1580,plain,
% 0.60/0.80 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1581,plain,
% 0.60/0.80 ((big_p(sk10) | (~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk7, sk6(sk7)))) <=> (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1582,plain,
% 0.60/0.80 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1581])).
% 0.60/0.80 tff(1583,plain,
% 0.60/0.80 (((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1582, 1580])).
% 0.60/0.80 tff(1584,plain,
% 0.60/0.80 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | (big_p(sk10) | (~big_p(sk9)) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1585,plain,
% 0.60/0.80 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.60/0.80 tff(1586,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1585, 493, 1457, 504, 1529, 1527, 1579])).
% 0.60/0.80 tff(1587,plain,(big_p(sk1(sk7)) | big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1588,plain,
% 0.60/0.80 (big_p(sk1(sk7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1587, 493])).
% 0.60/0.80 tff(1589,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1585, 493, 1457, 504, 1542, 1540, 1579])).
% 0.60/0.80 tff(1590,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1591,plain,
% 0.60/0.80 (big_r(sk2(sk7), sk1(sk7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1590, 493])).
% 0.60/0.80 tff(1592,plain,
% 0.60/0.80 (~big_r(sk7, sk2(sk7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[520, 493, 1457, 504, 1591, 1588])).
% 0.60/0.80 tff(1593,plain,
% 0.60/0.80 (big_r(sk7, sk6(sk7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1548, 1592])).
% 0.60/0.80 tff(1594,plain,
% 0.60/0.80 (big_r(sk6(sk7), sk5(sk7))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1550, 1592])).
% 0.60/0.80 tff(1595,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1585, 493, 1457, 504, 1594, 1593, 1579])).
% 0.60/0.80 tff(1596,plain,(big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1597,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1598,plain,
% 0.60/0.80 (((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1599,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1598])).
% 0.60/0.80 tff(1600,plain,
% 0.60/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1599, 1597])).
% 0.60/0.80 tff(1601,plain,
% 0.60/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1602,plain,
% 0.60/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : ((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.60/0.80 tff(1603,plain,
% 0.60/0.80 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1602, 1026, 9, 1515, 1553, 1163])).
% 0.60/0.80 tff(1604,plain,
% 0.60/0.80 (big_p(sk5(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1603, 193, 1596])).
% 0.60/0.80 tff(1605,assumption,(~big_r(sk7, sk6(sk7))), introduced(assumption)).
% 0.60/0.80 tff(1606,plain,
% 0.60/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1607,plain,
% 0.60/0.80 (((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1608,plain,
% 0.60/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1607])).
% 0.60/0.80 tff(1609,plain,
% 0.60/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1608, 1606])).
% 0.60/0.80 tff(1610,plain,
% 0.60/0.80 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk9)) | (~big_p(sk10)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1611,plain,
% 0.60/0.80 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 0.60/0.80 tff(1612,plain,
% 0.60/0.80 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_p(sk1(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1611, 840, 9, 1515, 1553, 1163])).
% 0.60/0.80 tff(1613,plain,
% 0.60/0.80 (big_p(sk1(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1612, 1605, 1596])).
% 0.60/0.80 tff(1614,plain,
% 0.60/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1615,plain,
% 0.60/0.80 (((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1616,plain,
% 0.60/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1615])).
% 0.60/0.80 tff(1617,plain,
% 0.60/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7)))) <=> ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1616, 1614])).
% 0.60/0.80 tff(1618,plain,
% 0.60/0.80 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1619,plain,
% 0.60/0.80 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.60/0.80 tff(1620,plain,
% 0.60/0.80 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_p(sk5(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1619, 1008, 9, 1515, 1553, 1163])).
% 0.60/0.80 tff(1621,plain,
% 0.60/0.80 (big_p(sk5(sk9))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1620, 6, 1596])).
% 0.60/0.80 tff(1622,assumption,(~big_r(sk6(sk7), sk5(sk7))), introduced(assumption)).
% 0.60/0.80 tff(1623,plain,
% 0.60/0.80 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1624,plain,
% 0.60/0.80 (((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1625,plain,
% 0.60/0.81 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1624])).
% 0.60/0.81 tff(1626,plain,
% 0.60/0.81 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1625, 1623])).
% 0.60/0.81 tff(1627,plain,
% 0.60/0.81 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1628,plain,
% 0.60/0.81 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 0.60/0.81 tff(1629,plain,
% 0.60/0.81 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1628, 960, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1630,plain,
% 0.60/0.81 (big_p(sk1(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1629, 1622, 1596])).
% 0.60/0.81 tff(1631,plain,
% 0.60/0.81 (big_p(sk1(sk7))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1528, 1622])).
% 0.60/0.81 tff(1632,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1633,plain,
% 0.60/0.81 (((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1634,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1633])).
% 0.60/0.81 tff(1635,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1634, 1632])).
% 0.60/0.81 tff(1636,plain,
% 0.60/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1637,plain,
% 0.60/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 0.60/0.81 tff(1638,plain,
% 0.60/0.81 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1637, 938, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1639,plain,
% 0.60/0.81 (big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1638, 1622, 1596])).
% 0.60/0.81 tff(1640,plain,
% 0.60/0.81 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1641,plain,
% 0.60/0.81 (((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1642,plain,
% 0.60/0.81 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1641])).
% 0.60/0.81 tff(1643,plain,
% 0.60/0.81 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1642, 1640])).
% 0.60/0.81 tff(1644,plain,
% 0.60/0.81 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1645,plain,
% 0.60/0.81 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 0.60/0.81 tff(1646,plain,
% 0.60/0.81 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1645, 978, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1647,plain,
% 0.60/0.81 (big_r(sk9, sk2(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1646, 1622, 1596])).
% 0.60/0.81 tff(1648,plain,
% 0.60/0.81 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1649,plain,
% 0.60/0.81 (((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1650,plain,
% 0.60/0.81 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1649])).
% 0.60/0.81 tff(1651,plain,
% 0.60/0.81 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1650, 1648])).
% 0.60/0.81 tff(1652,plain,
% 0.60/0.81 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1653,plain,
% 0.60/0.81 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 0.60/0.81 tff(1654,plain,
% 0.60/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1653, 918, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1655,plain,
% 0.60/0.81 (big_p(sk5(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1654, 394, 1596])).
% 0.60/0.81 tff(1656,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1657,plain,
% 0.60/0.81 (((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1658,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1657])).
% 0.60/0.81 tff(1659,plain,
% 0.60/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1658, 1656])).
% 0.60/0.81 tff(1660,plain,
% 0.60/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | ((~big_p(a)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1661,plain,
% 0.60/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 0.60/0.81 tff(1662,plain,
% 0.60/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1661, 938, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1663,plain,
% 0.60/0.81 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1662, 394, 1596])).
% 0.60/0.81 tff(1664,plain,
% 0.60/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1665,plain,
% 0.60/0.81 (((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1666,plain,
% 0.60/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1665])).
% 0.60/0.81 tff(1667,plain,
% 0.60/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1666, 1664])).
% 0.60/0.81 tff(1668,plain,
% 0.60/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1669,plain,
% 0.60/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 0.60/0.81 tff(1670,plain,
% 0.60/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1669, 859, 9, 1515, 1553, 1163])).
% 0.60/0.81 tff(1671,plain,
% 0.60/0.81 (big_r(sk9, sk6(sk9))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1670, 394, 1596])).
% 0.60/0.81 tff(1672,plain,
% 0.60/0.81 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1673,plain,
% 0.60/0.81 (((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk6(sk9)))) <=> ((~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1674,plain,
% 0.60/0.81 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1673])).
% 0.60/0.82 tff(1675,plain,
% 0.60/0.82 (((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk6(sk9))))) <=> ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1674, 1672])).
% 0.60/0.82 tff(1676,plain,
% 0.60/0.82 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | ((~big_p(sk5(sk9))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7))) | (~big_r(sk9, sk6(sk9))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1677,plain,
% 0.60/0.82 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))) | (~big_r(sk7, sk6(sk7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.60/0.82 tff(1678,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1677, 250, 1671, 1663, 1542, 1540, 1579, 1655])).
% 0.60/0.82 tff(1679,plain,(big_r(sk2(sk7), sk1(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1680,plain,
% 0.60/0.82 (big_r(sk7, sk2(sk7))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1550, 1622])).
% 0.60/0.82 tff(1681,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[280, 250, 1680, 1679, 1647, 1639, 1631, 1630])).
% 0.60/0.82 tff(1682,plain,(big_r(sk6(sk7), sk5(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1683,plain,
% 0.60/0.82 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1684,plain,
% 0.60/0.82 (((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1685,plain,
% 0.60/0.82 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1684])).
% 0.60/0.82 tff(1686,plain,
% 0.60/0.82 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1685, 1683])).
% 0.60/0.82 tff(1687,plain,
% 0.60/0.82 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(a)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1688,plain,
% 0.60/0.82 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 0.60/0.82 tff(1689,plain,
% 0.60/0.82 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1688, 960, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1690,plain,
% 0.60/0.82 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1689, 6, 1596])).
% 0.60/0.82 tff(1691,plain,
% 0.60/0.82 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1692,plain,
% 0.60/0.82 (((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1693,plain,
% 0.60/0.82 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1692])).
% 0.60/0.82 tff(1694,plain,
% 0.60/0.82 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1693, 1691])).
% 0.60/0.82 tff(1695,plain,
% 0.60/0.82 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(a)) | big_p(sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1696,plain,
% 0.60/0.82 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : ((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 0.60/0.82 tff(1697,plain,
% 0.60/0.82 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1696, 840, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1698,plain,
% 0.60/0.82 (big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1697, 6, 1596])).
% 0.60/0.82 tff(1699,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1677, 250, 1698, 1690, 1682, 1527, 1579, 1621])).
% 0.60/0.82 tff(1700,plain,(big_p(sk1(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1701,plain,
% 0.60/0.82 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1702,plain,
% 0.60/0.82 (((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1703,plain,
% 0.60/0.82 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1702])).
% 0.60/0.82 tff(1704,plain,
% 0.60/0.82 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1703, 1701])).
% 0.60/0.82 tff(1705,plain,
% 0.60/0.82 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1706,plain,
% 0.60/0.82 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 0.60/0.82 tff(1707,plain,
% 0.60/0.82 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1706, 859, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1708,plain,
% 0.60/0.82 (big_r(sk2(sk9), sk1(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1707, 1605, 1596])).
% 0.60/0.82 tff(1709,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1710,plain,
% 0.60/0.82 (((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7))) <=> ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1711,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1710])).
% 0.60/0.82 tff(1712,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1711, 1709])).
% 0.60/0.82 tff(1713,plain,
% 0.60/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1714,plain,
% 0.60/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 0.60/0.82 tff(1715,plain,
% 0.60/0.82 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_r(sk9, sk2(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1714, 877, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1716,plain,
% 0.60/0.82 (big_r(sk9, sk2(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1715, 1605, 1596])).
% 0.60/0.82 tff(1717,plain,
% 0.60/0.82 (big_r(sk7, sk2(sk7))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1548, 1605])).
% 0.60/0.82 tff(1718,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[280, 250, 1717, 1679, 1716, 1708, 1700, 1613])).
% 0.60/0.82 tff(1719,plain,(big_r(sk7, sk6(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1720,plain,
% 0.60/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1721,plain,
% 0.60/0.82 (((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1722,plain,
% 0.60/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1721])).
% 0.60/0.82 tff(1723,plain,
% 0.60/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))) <=> ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1722, 1720])).
% 0.60/0.82 tff(1724,plain,
% 0.60/0.82 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1725,plain,
% 0.60/0.82 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : ((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 0.60/0.82 tff(1726,plain,
% 0.60/0.82 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1725, 978, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1727,plain,
% 0.60/0.82 (big_r(sk6(sk9), sk5(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1726, 193, 1596])).
% 0.60/0.82 tff(1728,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1729,plain,
% 0.60/0.82 (((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))) <=> ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1730,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1729])).
% 0.60/0.82 tff(1731,plain,
% 0.60/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))) <=> ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1730, 1728])).
% 0.60/0.82 tff(1732,plain,
% 0.60/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(a)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1733,plain,
% 0.60/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(a)) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 0.60/0.82 tff(1734,plain,
% 0.60/0.82 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1733, 877, 9, 1515, 1553, 1163])).
% 0.60/0.82 tff(1735,plain,
% 0.60/0.82 (big_r(sk9, sk6(sk9))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1734, 193, 1596])).
% 0.60/0.82 tff(1736,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1677, 250, 1735, 1727, 1682, 1719, 1579, 1604])).
% 0.60/0.82 tff(1737,plain,(big_r(sk7, sk2(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.83 tff(1738,plain,
% 0.66/0.83 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[924, 918, 9, 1553])).
% 0.66/0.83 tff(1739,plain,
% 0.66/0.83 (big_p(sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1738, 91, 1596])).
% 0.66/0.83 tff(1740,plain,
% 0.66/0.83 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[944, 938, 9, 1553])).
% 0.66/0.83 tff(1741,plain,
% 0.66/0.83 (big_r(sk6(sk9), sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1740, 91, 1596])).
% 0.66/0.83 tff(1742,plain,
% 0.66/0.83 (big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_p(sk10))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[889, 1553])).
% 0.66/0.83 tff(1743,plain,
% 0.66/0.83 (big_r(sk9, sk6(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1742, 1737, 1596, 1679, 1700])).
% 0.66/0.83 tff(1744,plain,
% 0.66/0.83 ($false),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[997, 250, 1737, 1679, 1700, 1743, 1741, 1739])).
% 0.66/0.83 tff(1745,plain,(big_r(sk2(sk9), sk1(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.83 tff(1746,plain,
% 0.66/0.83 (big_r(sk6(sk9), sk5(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_p(sk10))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[990, 1553])).
% 0.66/0.83 tff(1747,plain,
% 0.66/0.83 (big_r(sk6(sk9), sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1746, 1745, 1679, 1700, 1596, 1737])).
% 0.66/0.83 tff(1748,plain,
% 0.66/0.83 (~big_p(sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[997, 250, 1737, 1679, 1700, 1743, 1747])).
% 0.66/0.83 tff(1749,plain,
% 0.66/0.83 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1032, 1026, 9, 1553])).
% 0.66/0.83 tff(1750,plain,
% 0.66/0.83 (big_r(sk9, sk2(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1749, 1748, 1596])).
% 0.66/0.83 tff(1751,plain,
% 0.66/0.83 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1014, 1008, 9, 1553])).
% 0.66/0.83 tff(1752,plain,
% 0.66/0.83 (big_p(sk1(sk9))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1751, 1748, 1596])).
% 0.66/0.83 tff(1753,plain,
% 0.66/0.83 ((~big_p(sk1(sk9))) | (~big_r(sk9, sk2(sk9)))),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[280, 250, 1737, 1679, 1745, 1700])).
% 0.66/0.83 tff(1754,plain,
% 0.66/0.83 ($false),
% 0.66/0.83 inference(unit_resolution,[status(thm)],[1753, 1752, 1750])).
% 0.66/0.83 % SZS output end Proof
% 0.66/0.83 % E exiting
%------------------------------------------------------------------------------