TSTP Solution File: SYN067-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN067-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.59s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN067-3 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:42:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.59 % SZS status Unsatisfiable
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 tff(big_r_type, type, (
% 0.20/0.59 big_r: ( $i * $i ) > $o)).
% 0.20/0.59 tff(sk2_type, type, (
% 0.20/0.59 sk2: $i > $i)).
% 0.20/0.59 tff(sk9_type, type, (
% 0.20/0.59 sk9: $i)).
% 0.20/0.59 tff(big_p_type, type, (
% 0.20/0.59 big_p: $i > $o)).
% 0.20/0.59 tff(sk10_type, type, (
% 0.20/0.59 sk10: $i)).
% 0.20/0.59 tff(sk5_type, type, (
% 0.20/0.59 sk5: $i > $i)).
% 0.20/0.59 tff(sk7_type, type, (
% 0.20/0.59 sk7: $i)).
% 0.20/0.59 tff(sk1_type, type, (
% 0.20/0.59 sk1: $i > $i)).
% 0.20/0.59 tff(sk8_type, type, (
% 0.20/0.59 sk8: $i)).
% 0.20/0.59 tff(sk3_type, type, (
% 0.20/0.59 sk3: $i > $i)).
% 0.20/0.59 tff(a_type, type, (
% 0.20/0.59 a: $i)).
% 0.20/0.59 tff(sk4_type, type, (
% 0.20/0.59 sk4: $i > $i)).
% 0.20/0.59 tff(sk6_type, type, (
% 0.20/0.59 sk6: $i > $i)).
% 0.20/0.59 tff(1,assumption,(~big_p(sk5(sk7))), introduced(assumption)).
% 0.20/0.59 tff(2,assumption,(~big_p(sk8)), introduced(assumption)).
% 0.20/0.59 tff(3,assumption,(~big_r(sk9, sk2(sk9))), introduced(assumption)).
% 0.20/0.59 tff(4,assumption,(~big_p(sk7)), introduced(assumption)).
% 0.20/0.59 tff(5,assumption,(~big_p(sk9)), introduced(assumption)).
% 0.20/0.59 tff(6,assumption,(~big_p(sk1(sk7))), introduced(assumption)).
% 0.20/0.59 tff(7,plain,
% 0.20/0.59 (^[B: $i, A: $i] : refl((big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(8,plain,
% 0.20/0.59 (![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.59 tff(9,plain,
% 0.20/0.59 (![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(10,plain,
% 0.20/0.59 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)) <=> ($false | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A)))), rewrite(($false | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | 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)) <=> (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(11,plain,
% 0.20/0.59 (![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(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.59 tff(12,plain,
% 0.20/0.59 (^[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))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(13,plain,
% 0.20/0.59 (![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))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.59 tff(14,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/sandbox/benchmark/theBenchmark.p','pel38_1')).
% 0.20/0.59 tff(15,plain,
% 0.20/0.59 (![B: $i, A: $i] : ((~big_p(a)) | big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.59 tff(16,plain,
% 0.20/0.59 (![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.59 tff(17,plain,
% 0.20/0.59 (![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.59 tff(18,plain,(
% 0.20/0.59 ![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(skolemize,[status(sab)],[17])).
% 0.20/0.59 tff(19,plain,
% 0.20/0.59 (![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.59 tff(20,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(21,plain,
% 0.20/0.59 ((big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7)) <=> (big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(22,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.59 tff(23,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.59 tff(24,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk7)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(25,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk7) | big_p(sk3(sk7)) | big_p(sk1(sk7))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.59 tff(26,plain,
% 0.20/0.59 (big_p(sk3(sk7)) | big_p(sk1(sk7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[25, 19, 4])).
% 0.20/0.59 tff(27,plain,
% 0.20/0.59 (big_p(sk3(sk7))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[26, 6])).
% 0.20/0.59 tff(28,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(29,plain,
% 0.20/0.59 ((big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9)) <=> (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(30,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.59 tff(31,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.59 tff(32,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk7) | big_p(sk9))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(33,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.59 tff(34,plain,
% 0.20/0.59 (big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[33, 19, 5, 4])).
% 0.20/0.59 tff(35,plain,
% 0.20/0.59 (big_p(sk3(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[34, 6])).
% 0.20/0.59 tff(36,plain,
% 0.20/0.59 (^[I: $i, J: $i] : refl((big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(37,plain,
% 0.20/0.59 (![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.59 tff(38,plain,
% 0.20/0.59 (![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(39,plain,
% 0.20/0.59 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ($false | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))))), rewrite(($false | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> (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))) <=> (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(40,plain,
% 0.20/0.59 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I))) <=> ![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.59 tff(41,plain,
% 0.20/0.59 (^[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)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(42,plain,
% 0.20/0.59 (![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)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.59 tff(43,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/sandbox/benchmark/theBenchmark.p','pel38_5')).
% 0.20/0.59 tff(44,plain,
% 0.20/0.59 (![I: $i, J: $i] : ((~big_p(a)) | big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.59 tff(45,plain,
% 0.20/0.59 (![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.59 tff(46,plain,
% 0.20/0.59 (![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.59 tff(47,plain,(
% 0.20/0.59 ![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(skolemize,[status(sab)],[46])).
% 0.20/0.59 tff(48,plain,
% 0.20/0.59 (![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.20/0.59 tff(49,plain,
% 0.20/0.59 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(50,plain,
% 0.20/0.59 ((big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9))) <=> (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(51,plain,
% 0.20/0.59 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.59 tff(52,plain,
% 0.20/0.59 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.59 tff(53,plain,
% 0.20/0.59 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(54,plain,
% 0.20/0.59 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.59 tff(55,plain,
% 0.20/0.59 (big_r(sk9, sk4(sk9)) | big_r(sk9, sk2(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[54, 48, 5])).
% 0.20/0.59 tff(56,plain,
% 0.20/0.59 (big_r(sk9, sk4(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[55, 3])).
% 0.20/0.59 tff(57,assumption,(~big_r(sk4(sk7), sk3(sk7))), introduced(assumption)).
% 0.20/0.59 tff(58,plain,
% 0.20/0.59 (^[E: $i, F: $i] : refl((big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(59,plain,
% 0.20/0.59 (![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.59 tff(60,plain,
% 0.20/0.59 (![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(61,plain,
% 0.20/0.59 (^[E: $i, F: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> ($false | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))))), rewrite(($false | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F))) <=> (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))) <=> (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(62,plain,
% 0.20/0.59 (![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(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.59 tff(63,plain,
% 0.20/0.59 (^[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)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(64,plain,
% 0.20/0.59 (![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)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.59 tff(65,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/sandbox/benchmark/theBenchmark.p','pel38_3')).
% 0.20/0.59 tff(66,plain,
% 0.20/0.59 (![E: $i, F: $i] : ((~big_p(a)) | big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.59 tff(67,plain,
% 0.20/0.59 (![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.59 tff(68,plain,
% 0.20/0.59 (![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.59 tff(69,plain,(
% 0.20/0.59 ![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(skolemize,[status(sab)],[68])).
% 0.20/0.59 tff(70,plain,
% 0.20/0.59 (![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.59 tff(71,plain,
% 0.20/0.59 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(72,plain,
% 0.20/0.59 ((big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(73,plain,
% 0.20/0.59 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.59 tff(74,plain,
% 0.20/0.59 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.59 tff(75,plain,
% 0.20/0.59 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(76,plain,
% 0.20/0.59 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.59 tff(77,plain,
% 0.20/0.59 (big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[76, 70, 5, 4])).
% 0.20/0.59 tff(78,plain,
% 0.20/0.59 (big_p(sk1(sk9))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[77, 57])).
% 0.20/0.59 tff(79,plain,
% 0.20/0.59 (^[L: $i, K: $i] : refl((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))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(80,plain,
% 0.20/0.59 (![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.59 tff(81,plain,
% 0.20/0.59 (![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(82,plain,
% 0.20/0.59 (^[L: $i, K: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))) <=> ($false | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K))))), rewrite(($false | 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(a)) | 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)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(83,plain,
% 0.20/0.59 (![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(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.59 tff(84,plain,
% 0.20/0.59 (^[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)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(85,plain,
% 0.20/0.59 (![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)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.59 tff(86,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/sandbox/benchmark/theBenchmark.p','pel38_6')).
% 0.20/0.59 tff(87,plain,
% 0.20/0.59 (![L: $i, K: $i] : ((~big_p(a)) | big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.59 tff(88,plain,
% 0.20/0.59 (![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.59 tff(89,plain,
% 0.20/0.59 (![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.59 tff(90,plain,(
% 0.20/0.59 ![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.60 inference(skolemize,[status(sab)],[89])).
% 0.20/0.60 tff(91,plain,
% 0.20/0.60 (![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.20/0.60 tff(92,plain,
% 0.20/0.60 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(93,plain,
% 0.20/0.60 ((big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(94,plain,
% 0.20/0.60 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.60 tff(95,plain,
% 0.20/0.60 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.20/0.60 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.60 tff(96,plain,
% 0.20/0.60 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk7), sk3(sk7)))),
% 0.20/0.60 inference(quant_inst,[status(thm)],[])).
% 0.20/0.60 tff(97,plain,
% 0.20/0.60 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.60 tff(98,plain,
% 0.20/0.60 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[97, 91, 5, 4])).
% 0.20/0.60 tff(99,plain,
% 0.20/0.60 (big_r(sk9, sk2(sk9))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[98, 57])).
% 0.20/0.60 tff(100,assumption,(~big_r(sk2(sk9), sk1(sk9))), introduced(assumption)).
% 0.20/0.60 tff(101,plain,
% 0.20/0.60 (^[E1: $i, F1: $i] : refl((big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(102,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)) <=> ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.60 tff(103,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1)) <=> ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(104,plain,
% 0.20/0.60 (^[E1: $i, F1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), ((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)) | $false | big_p(E1) | big_p(F1)))), rewrite((big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | $false | big_p(E1) | big_p(F1)) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | 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)) <=> (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(105,plain,
% 0.20/0.60 (![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(E1) | big_p(F1))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.60 tff(106,plain,
% 0.20/0.60 (^[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))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(107,plain,
% 0.20/0.60 (![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))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.60 tff(108,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/sandbox/benchmark/theBenchmark.p','pel38_13')).
% 0.20/0.60 tff(109,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | (~big_p(a)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.60 tff(110,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.60 tff(111,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.60 tff(112,plain,(
% 0.20/0.60 ![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(skolemize,[status(sab)],[111])).
% 0.20/0.60 tff(113,plain,
% 0.20/0.60 (![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.20/0.60 tff(114,plain,
% 0.20/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | 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(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(115,plain,
% 0.20/0.60 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk9)) <=> (big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(116,plain,
% 0.20/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.60 tff(117,plain,
% 0.20/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.58/0.60 inference(transitivity,[status(thm)],[116, 114])).
% 0.58/0.60 tff(118,plain,
% 0.58/0.60 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk9))),
% 0.58/0.60 inference(quant_inst,[status(thm)],[])).
% 0.58/0.60 tff(119,plain,
% 0.58/0.60 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.58/0.60 tff(120,plain,
% 0.58/0.60 (big_p(sk3(sk7))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[119, 113, 5, 4, 100])).
% 0.58/0.60 tff(121,plain,
% 0.58/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | 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(E1) | big_p(F1))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(122,plain,
% 0.58/0.60 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9)) <=> (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(123,plain,
% 0.58/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))))),
% 0.58/0.60 inference(monotonicity,[status(thm)],[122])).
% 0.58/0.60 tff(124,plain,
% 0.58/0.60 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)))),
% 0.58/0.60 inference(transitivity,[status(thm)],[123, 121])).
% 0.58/0.60 tff(125,plain,
% 0.58/0.60 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9))),
% 0.58/0.60 inference(quant_inst,[status(thm)],[])).
% 0.58/0.60 tff(126,plain,
% 0.58/0.60 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.58/0.60 tff(127,plain,
% 0.58/0.60 (big_p(sk3(sk9))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[126, 113, 5, 100])).
% 0.58/0.60 tff(128,plain,
% 0.58/0.60 (^[H1: $i, G1: $i] : refl((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))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(129,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[128])).
% 0.58/0.60 tff(130,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(131,plain,
% 0.58/0.60 (^[H1: $i, G1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ($false | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))))), rewrite(($false | 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(a)) | 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)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(132,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1))) <=> ![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[131])).
% 0.58/0.60 tff(133,plain,
% 0.58/0.60 (^[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)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(134,plain,
% 0.58/0.60 (![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)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[133])).
% 0.58/0.60 tff(135,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/sandbox/benchmark/theBenchmark.p','pel38_14')).
% 0.58/0.60 tff(136,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : ((~big_p(a)) | big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.58/0.60 tff(137,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.58/0.60 tff(138,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.58/0.60 tff(139,plain,(
% 0.58/0.60 ![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(skolemize,[status(sab)],[138])).
% 0.58/0.60 tff(140,plain,
% 0.58/0.60 (![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.58/0.60 tff(141,plain,
% 0.58/0.60 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(142,plain,
% 0.58/0.60 ((big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(143,plain,
% 0.58/0.60 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))))),
% 0.58/0.60 inference(monotonicity,[status(thm)],[142])).
% 0.58/0.60 tff(144,plain,
% 0.58/0.60 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9)))),
% 0.58/0.60 inference(transitivity,[status(thm)],[143, 141])).
% 0.58/0.60 tff(145,plain,
% 0.58/0.60 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.58/0.60 inference(quant_inst,[status(thm)],[])).
% 0.58/0.60 tff(146,plain,
% 0.58/0.60 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.58/0.60 tff(147,plain,
% 0.58/0.60 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk4(sk9))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[146, 140, 5])).
% 0.58/0.60 tff(148,plain,
% 0.58/0.60 (big_r(sk9, sk4(sk9))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[147, 100])).
% 0.58/0.60 tff(149,plain,
% 0.58/0.60 (^[J1: $i, I1: $i] : refl((big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(150,plain,
% 0.58/0.60 (![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[149])).
% 0.58/0.60 tff(151,plain,
% 0.58/0.60 (![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(152,plain,
% 0.58/0.60 (^[J1: $i, I1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> ($false | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))))), rewrite(($false | big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1))) <=> (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))) <=> (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(153,plain,
% 0.58/0.60 (![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(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[152])).
% 0.58/0.60 tff(154,plain,
% 0.58/0.60 (^[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)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(155,plain,
% 0.58/0.60 (![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)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[154])).
% 0.58/0.60 tff(156,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/sandbox/benchmark/theBenchmark.p','pel38_15')).
% 0.58/0.60 tff(157,plain,
% 0.58/0.60 (![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)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.58/0.60 tff(158,plain,
% 0.58/0.60 (![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.58/0.60 tff(159,plain,
% 0.58/0.60 (![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.58/0.60 tff(160,plain,(
% 0.58/0.60 ![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(skolemize,[status(sab)],[159])).
% 0.58/0.60 tff(161,plain,
% 0.58/0.60 (![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[160, 150])).
% 0.58/0.60 tff(162,plain,
% 0.58/0.60 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(163,plain,
% 0.58/0.60 ((big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(164,plain,
% 0.58/0.60 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.58/0.60 inference(monotonicity,[status(thm)],[163])).
% 0.58/0.60 tff(165,plain,
% 0.58/0.60 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.58/0.60 inference(transitivity,[status(thm)],[164, 162])).
% 0.58/0.60 tff(166,plain,
% 0.58/0.60 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.58/0.60 inference(quant_inst,[status(thm)],[])).
% 0.58/0.60 tff(167,plain,
% 0.58/0.60 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.58/0.60 tff(168,plain,
% 0.58/0.60 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk4(sk9), sk3(sk9))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[167, 161, 5])).
% 0.58/0.60 tff(169,plain,
% 0.58/0.60 (big_r(sk4(sk9), sk3(sk9))),
% 0.58/0.60 inference(unit_resolution,[status(thm)],[168, 100])).
% 0.58/0.60 tff(170,assumption,(~big_r(sk7, sk4(sk7))), introduced(assumption)).
% 0.58/0.60 tff(171,plain,
% 0.58/0.60 (^[D: $i, C: $i] : refl((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))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(172,plain,
% 0.58/0.60 (![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[171])).
% 0.58/0.60 tff(173,plain,
% 0.58/0.60 (![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(174,plain,
% 0.58/0.60 (^[D: $i, C: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))) <=> ($false | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C))))), rewrite(($false | 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(a)) | 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)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(175,plain,
% 0.58/0.60 (![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(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[174])).
% 0.58/0.60 tff(176,plain,
% 0.58/0.60 (^[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)))))),
% 0.58/0.60 inference(bind,[status(th)],[])).
% 0.58/0.60 tff(177,plain,
% 0.58/0.60 (![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)))),
% 0.58/0.60 inference(quant_intro,[status(thm)],[176])).
% 0.58/0.60 tff(178,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/sandbox/benchmark/theBenchmark.p','pel38_2')).
% 0.58/0.60 tff(179,plain,
% 0.58/0.60 (![D: $i, C: $i] : ((~big_p(a)) | big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.58/0.60 tff(180,plain,
% 0.58/0.60 (![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.58/0.60 tff(181,plain,
% 0.58/0.60 (![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.58/0.60 tff(182,plain,(
% 0.58/0.60 ![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(skolemize,[status(sab)],[181])).
% 0.58/0.60 tff(183,plain,
% 0.58/0.60 (![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))),
% 0.58/0.60 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.58/0.60 tff(184,plain,
% 0.58/0.60 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(185,plain,
% 0.58/0.60 ((big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7))) <=> (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.58/0.60 inference(rewrite,[status(thm)],[])).
% 0.58/0.60 tff(186,plain,
% 0.58/0.60 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[185])).
% 0.58/0.61 tff(187,plain,
% 0.58/0.61 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[186, 184])).
% 0.58/0.61 tff(188,plain,
% 0.58/0.61 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(189,plain,
% 0.58/0.61 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.58/0.61 tff(190,plain,
% 0.58/0.61 (big_p(sk1(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[189, 183, 4, 170])).
% 0.58/0.61 tff(191,plain,
% 0.58/0.61 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(192,plain,
% 0.58/0.61 ((big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(193,plain,
% 0.58/0.61 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[192])).
% 0.58/0.61 tff(194,plain,
% 0.58/0.61 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[193, 191])).
% 0.58/0.61 tff(195,plain,
% 0.58/0.61 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(196,plain,
% 0.58/0.61 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.58/0.61 tff(197,plain,
% 0.58/0.61 (big_p(sk1(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[196, 183, 5, 4, 170])).
% 0.58/0.61 tff(198,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(199,plain,
% 0.58/0.61 ((big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(200,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[199])).
% 0.58/0.61 tff(201,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[200, 198])).
% 0.58/0.61 tff(202,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(203,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.58/0.61 tff(204,plain,
% 0.58/0.61 (big_r(sk7, sk4(sk7)) | big_r(sk9, sk2(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[203, 48, 5, 4])).
% 0.58/0.61 tff(205,plain,
% 0.58/0.61 (big_r(sk9, sk2(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[204, 170])).
% 0.58/0.61 tff(206,plain,
% 0.58/0.61 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(207,plain,
% 0.58/0.61 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(208,plain,
% 0.58/0.61 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.58/0.61 tff(209,plain,
% 0.58/0.61 (big_r(sk7, sk4(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[208, 140, 5, 4])).
% 0.58/0.61 tff(210,plain,
% 0.58/0.61 (big_r(sk2(sk9), sk1(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[209, 170])).
% 0.58/0.61 tff(211,assumption,(~big_r(sk7, sk2(sk7))), introduced(assumption)).
% 0.58/0.61 tff(212,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(213,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(214,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.58/0.61 tff(215,plain,
% 0.58/0.61 (big_r(sk9, sk4(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[214, 48, 5, 4, 211])).
% 0.58/0.61 tff(216,plain,
% 0.58/0.61 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(217,plain,
% 0.58/0.61 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(218,plain,
% 0.58/0.61 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.58/0.61 tff(219,plain,
% 0.58/0.61 (big_r(sk4(sk9), sk3(sk9))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[218, 91, 5, 4, 211])).
% 0.58/0.61 tff(220,plain,
% 0.58/0.61 (^[H: $i, G: $i] : refl((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))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(221,plain,
% 0.58/0.61 (![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[220])).
% 0.58/0.61 tff(222,plain,
% 0.58/0.61 (![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(223,plain,
% 0.58/0.61 (^[H: $i, G: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))) <=> ($false | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H))))), rewrite(($false | 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(a)) | 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)))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(224,plain,
% 0.58/0.61 (![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(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[223])).
% 0.58/0.61 tff(225,plain,
% 0.58/0.61 (^[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)))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(226,plain,
% 0.58/0.61 (![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)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[225])).
% 0.58/0.61 tff(227,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/sandbox/benchmark/theBenchmark.p','pel38_4')).
% 0.58/0.61 tff(228,plain,
% 0.58/0.61 (![H: $i, G: $i] : ((~big_p(a)) | big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.58/0.61 tff(229,plain,
% 0.58/0.61 (![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.58/0.61 tff(230,plain,
% 0.58/0.61 (![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.58/0.61 tff(231,plain,(
% 0.58/0.61 ![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(skolemize,[status(sab)],[230])).
% 0.58/0.61 tff(232,plain,
% 0.58/0.61 (![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[231, 221])).
% 0.58/0.61 tff(233,plain,
% 0.58/0.61 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(234,plain,
% 0.58/0.61 ((big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7))) <=> (big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(235,plain,
% 0.58/0.61 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[234])).
% 0.58/0.61 tff(236,plain,
% 0.58/0.61 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[235, 233])).
% 0.58/0.61 tff(237,plain,
% 0.58/0.61 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(238,plain,
% 0.58/0.61 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.58/0.61 tff(239,plain,
% 0.58/0.61 (big_p(sk3(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[238, 232, 4, 211])).
% 0.58/0.61 tff(240,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(241,plain,
% 0.58/0.61 ((big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7))) <=> (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(242,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[241])).
% 0.58/0.61 tff(243,plain,
% 0.58/0.61 (((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[242, 240])).
% 0.58/0.61 tff(244,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(245,plain,
% 0.58/0.61 ((~![I: $i, J: $i] : (big_p(I) | big_p(J) | big_r(J, sk2(J)) | big_r(I, sk4(I)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.58/0.61 tff(246,plain,
% 0.58/0.61 (big_r(sk7, sk4(sk7)) | big_r(sk7, sk2(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[245, 48, 4])).
% 0.58/0.61 tff(247,plain,
% 0.58/0.61 (big_r(sk7, sk4(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[246, 211])).
% 0.58/0.61 tff(248,plain,
% 0.58/0.61 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(249,plain,
% 0.58/0.61 ((big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(250,plain,
% 0.58/0.61 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[249])).
% 0.58/0.61 tff(251,plain,
% 0.58/0.61 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7)))),
% 0.58/0.61 inference(transitivity,[status(thm)],[250, 248])).
% 0.58/0.61 tff(252,plain,
% 0.58/0.61 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_r(sk4(sk7), sk3(sk7)))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(253,plain,
% 0.58/0.61 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.58/0.61 tff(254,plain,
% 0.58/0.61 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk7, sk2(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[253, 91, 4])).
% 0.58/0.61 tff(255,plain,
% 0.58/0.61 (big_r(sk4(sk7), sk3(sk7))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[254, 211])).
% 0.58/0.61 tff(256,plain,
% 0.58/0.61 (^[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))))),
% 0.58/0.61 inference(bind,[status(th)],[])).
% 0.58/0.61 tff(257,plain,
% 0.58/0.61 (![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)))),
% 0.58/0.61 inference(quant_intro,[status(thm)],[256])).
% 0.58/0.61 tff(258,plain,
% 0.58/0.61 (![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)))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(259,plain,
% 0.58/0.61 (^[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)))))),
% 0.59/0.61 inference(bind,[status(th)],[])).
% 0.59/0.61 tff(260,plain,
% 0.59/0.61 (![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)))),
% 0.59/0.61 inference(quant_intro,[status(thm)],[259])).
% 0.59/0.61 tff(261,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/sandbox/benchmark/theBenchmark.p','pel38_46')).
% 0.59/0.61 tff(262,plain,
% 0.59/0.61 (![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)))),
% 0.59/0.61 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.59/0.61 tff(263,plain,
% 0.59/0.61 (![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)))),
% 0.59/0.61 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.59/0.61 tff(264,plain,(
% 0.59/0.61 ![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)))),
% 0.59/0.61 inference(skolemize,[status(sab)],[263])).
% 0.59/0.61 tff(265,plain,
% 0.59/0.61 (![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)))),
% 0.59/0.61 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.59/0.61 tff(266,plain,
% 0.59/0.61 (((~![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))))),
% 0.59/0.61 inference(rewrite,[status(thm)],[])).
% 0.59/0.61 tff(267,plain,
% 0.59/0.61 (((~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))))),
% 0.59/0.61 inference(rewrite,[status(thm)],[])).
% 0.59/0.61 tff(268,plain,
% 0.59/0.61 (((~![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)))))),
% 0.59/0.61 inference(monotonicity,[status(thm)],[267])).
% 0.59/0.61 tff(269,plain,
% 0.59/0.61 (((~![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))))),
% 0.59/0.62 inference(transitivity,[status(thm)],[268, 266])).
% 0.59/0.62 tff(270,plain,
% 0.59/0.62 ((~![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(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))))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(271,plain,
% 0.59/0.62 ((~![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(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)))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.59/0.62 tff(272,plain,
% 0.59/0.62 (~big_p(sk3(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[271, 265, 255, 247, 239, 219, 215])).
% 0.59/0.62 tff(273,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(274,plain,
% 0.59/0.62 ((big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(275,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[274])).
% 0.59/0.62 tff(276,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[275, 273])).
% 0.59/0.62 tff(277,plain,
% 0.59/0.62 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk7) | big_p(sk9) | big_r(sk7, sk2(sk7)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(278,plain,
% 0.59/0.62 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.59/0.62 tff(279,plain,
% 0.59/0.62 ($false),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[278, 232, 5, 4, 211, 272])).
% 0.59/0.62 tff(280,plain,(big_r(sk7, sk2(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.62 tff(281,plain,
% 0.59/0.62 (big_r(sk7, sk2(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[280, 5, 4])).
% 0.59/0.62 tff(282,plain,
% 0.59/0.62 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(283,plain,
% 0.59/0.62 ((big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(284,plain,
% 0.59/0.62 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[283])).
% 0.59/0.62 tff(285,plain,
% 0.59/0.62 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[284, 282])).
% 0.59/0.62 tff(286,plain,
% 0.59/0.62 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk7, sk4(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(287,plain,
% 0.59/0.62 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.59/0.62 tff(288,plain,
% 0.59/0.62 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk4(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[287, 140, 4])).
% 0.59/0.62 tff(289,plain,
% 0.59/0.62 (big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[288, 170])).
% 0.59/0.62 tff(290,plain,
% 0.59/0.62 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(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(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(291,plain,
% 0.59/0.62 (((~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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(292,plain,
% 0.59/0.62 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk7, sk2(sk7)))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[291])).
% 0.59/0.62 tff(293,plain,
% 0.59/0.62 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk7, sk2(sk7))))),
% 0.59/0.62 inference(transitivity,[status(thm)],[292, 290])).
% 0.59/0.62 tff(294,plain,
% 0.59/0.62 ((~![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))))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(295,plain,
% 0.59/0.62 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_r(sk7, sk2(sk7)))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.59/0.62 tff(296,plain,
% 0.59/0.62 ((~big_p(sk1(sk7))) | (~big_p(sk1(sk9)))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[295, 265, 289, 281, 210, 205])).
% 0.59/0.62 tff(297,plain,
% 0.59/0.62 ($false),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[296, 197, 190])).
% 0.59/0.62 tff(298,plain,(big_r(sk7, sk4(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.62 tff(299,plain,
% 0.59/0.62 (big_r(sk7, sk4(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[298, 5, 4])).
% 0.59/0.62 tff(300,plain,
% 0.59/0.62 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(301,plain,
% 0.59/0.62 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(302,plain,
% 0.59/0.62 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.59/0.62 tff(303,plain,
% 0.59/0.62 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[302, 161, 5, 4])).
% 0.59/0.62 tff(304,plain,
% 0.59/0.62 (big_r(sk4(sk7), sk3(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[303, 100])).
% 0.59/0.62 tff(305,plain,
% 0.59/0.62 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[271, 265, 304, 299, 169, 148])).
% 0.59/0.62 tff(306,plain,
% 0.59/0.62 ($false),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[305, 127, 120])).
% 0.59/0.62 tff(307,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.62 tff(308,plain,
% 0.59/0.62 (big_r(sk2(sk9), sk1(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[307, 5, 4])).
% 0.59/0.62 tff(309,plain,
% 0.59/0.62 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(310,plain,
% 0.59/0.62 ((big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(311,plain,
% 0.59/0.62 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[310])).
% 0.59/0.62 tff(312,plain,
% 0.59/0.62 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[311, 309])).
% 0.59/0.62 tff(313,plain,
% 0.59/0.62 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(314,plain,
% 0.59/0.62 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.59/0.62 tff(315,plain,
% 0.59/0.62 (big_r(sk4(sk7), sk3(sk7)) | big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[314, 161, 4])).
% 0.59/0.62 tff(316,plain,
% 0.59/0.62 (big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[315, 57])).
% 0.59/0.62 tff(317,plain,
% 0.59/0.62 (~big_p(sk1(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[295, 265, 316, 281, 308, 99, 78])).
% 0.59/0.62 tff(318,plain,
% 0.59/0.62 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(319,plain,
% 0.59/0.62 ((big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(320,plain,
% 0.59/0.62 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[319])).
% 0.59/0.62 tff(321,plain,
% 0.59/0.62 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[320, 318])).
% 0.59/0.62 tff(322,plain,
% 0.59/0.62 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk7) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(323,plain,
% 0.59/0.62 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk7))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.59/0.62 tff(324,plain,
% 0.59/0.62 ($false),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[323, 70, 4, 57, 317])).
% 0.59/0.62 tff(325,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.62 tff(326,plain,
% 0.59/0.62 (big_r(sk4(sk7), sk3(sk7))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[325, 5, 4])).
% 0.59/0.62 tff(327,plain,
% 0.59/0.62 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(328,plain,
% 0.59/0.62 ((big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9))) <=> (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(329,plain,
% 0.59/0.62 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[328])).
% 0.59/0.62 tff(330,plain,
% 0.59/0.62 (((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[329, 327])).
% 0.59/0.62 tff(331,plain,
% 0.59/0.62 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | (big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(332,plain,
% 0.59/0.62 ((~![L: $i, K: $i] : (big_p(L) | big_p(K) | big_r(L, sk2(L)) | big_r(sk4(K), sk3(K)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.59/0.62 tff(333,plain,
% 0.59/0.62 (big_r(sk4(sk9), sk3(sk9)) | big_r(sk9, sk2(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[332, 91, 5])).
% 0.59/0.62 tff(334,plain,
% 0.59/0.62 (big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[333, 3])).
% 0.59/0.62 tff(335,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(336,plain,
% 0.59/0.62 ((big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9))) <=> (big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(337,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[336])).
% 0.59/0.62 tff(338,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[337, 335])).
% 0.59/0.62 tff(339,plain,
% 0.59/0.62 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.62 tff(340,plain,
% 0.59/0.62 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))),
% 0.59/0.62 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.59/0.62 tff(341,plain,
% 0.59/0.62 (big_r(sk9, sk2(sk9)) | big_p(sk3(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[340, 232, 5])).
% 0.59/0.62 tff(342,plain,
% 0.59/0.62 (big_p(sk3(sk9))),
% 0.59/0.62 inference(unit_resolution,[status(thm)],[341, 3])).
% 0.59/0.62 tff(343,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(344,plain,
% 0.59/0.62 ((big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9))) <=> (big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(rewrite,[status(thm)],[])).
% 0.59/0.62 tff(345,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))))),
% 0.59/0.62 inference(monotonicity,[status(thm)],[344])).
% 0.59/0.62 tff(346,plain,
% 0.59/0.62 (((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))) <=> ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(transitivity,[status(thm)],[345, 343])).
% 0.59/0.62 tff(347,plain,
% 0.59/0.62 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | (big_p(sk3(sk7)) | big_p(sk9) | big_p(sk7) | big_r(sk9, sk2(sk9)))),
% 0.59/0.62 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(348,plain,
% 0.59/0.63 ((~![H: $i, G: $i] : (big_p(sk3(G)) | big_p(H) | big_p(G) | big_r(H, sk2(H)))) | big_p(sk9) | big_p(sk7) | big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.59/0.63 tff(349,plain,
% 0.59/0.63 (big_p(sk3(sk7)) | big_r(sk9, sk2(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[348, 232, 5, 4])).
% 0.59/0.63 tff(350,plain,
% 0.59/0.63 (big_p(sk3(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[349, 3])).
% 0.59/0.63 tff(351,assumption,(big_r(sk9, sk4(sk9))), introduced(assumption)).
% 0.59/0.63 tff(352,assumption,(big_r(sk4(sk9), sk3(sk9))), introduced(assumption)).
% 0.59/0.63 tff(353,assumption,(big_r(sk4(sk7), sk3(sk7))), introduced(assumption)).
% 0.59/0.63 tff(354,plain,
% 0.59/0.63 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[271, 265, 353, 299, 352, 351])).
% 0.59/0.63 tff(355,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[354, 350, 342])).
% 0.59/0.63 tff(356,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,[]))).
% 0.59/0.63 tff(357,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[356, 334, 3, 326, 56, 5, 4])).
% 0.59/0.63 tff(358,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(359,plain,
% 0.59/0.63 (big_r(sk9, sk2(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[358, 5, 4])).
% 0.59/0.63 tff(360,assumption,(~big_r(sk9, sk4(sk9))), introduced(assumption)).
% 0.59/0.63 tff(361,plain,
% 0.59/0.63 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(362,plain,
% 0.59/0.63 ((big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9))) <=> (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(363,plain,
% 0.59/0.63 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[362])).
% 0.59/0.63 tff(364,plain,
% 0.59/0.63 (((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))) <=> ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[363, 361])).
% 0.59/0.63 tff(365,plain,
% 0.59/0.63 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | (big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9) | big_r(sk9, sk4(sk9)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(366,plain,
% 0.59/0.63 ((~![D: $i, C: $i] : (big_p(sk1(D)) | big_p(D) | big_p(C) | big_r(C, sk4(C)))) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.59/0.63 tff(367,plain,
% 0.59/0.63 (big_r(sk9, sk4(sk9)) | big_p(sk1(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[366, 183, 5])).
% 0.59/0.63 tff(368,plain,
% 0.59/0.63 (big_p(sk1(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[367, 360])).
% 0.59/0.63 tff(369,plain,
% 0.59/0.63 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(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(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(370,plain,
% 0.59/0.63 (((~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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(371,plain,
% 0.59/0.63 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[370])).
% 0.59/0.63 tff(372,plain,
% 0.59/0.63 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.59/0.63 inference(transitivity,[status(thm)],[371, 369])).
% 0.59/0.63 tff(373,plain,
% 0.59/0.63 ((~![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))))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(374,plain,
% 0.59/0.63 ((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.59/0.63 tff(375,plain,
% 0.59/0.63 ((~big_p(sk3(sk7))) | (~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[374, 265, 326, 299, 308])).
% 0.59/0.63 tff(376,plain,
% 0.59/0.63 (~big_p(sk3(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[375, 368, 359])).
% 0.59/0.63 tff(377,plain,
% 0.59/0.63 (((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(378,plain,
% 0.59/0.63 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | (big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(379,plain,
% 0.59/0.63 ((~![H1: $i, G1: $i] : (big_p(H1) | big_p(G1) | big_r(G1, sk4(G1)) | big_r(sk2(H1), sk1(H1)))) | big_p(sk7) | big_p(sk9) | big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.59/0.63 tff(380,plain,
% 0.59/0.63 (big_r(sk9, sk4(sk9)) | big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[379, 140, 5, 4])).
% 0.59/0.63 tff(381,plain,
% 0.59/0.63 (big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[380, 360])).
% 0.59/0.63 tff(382,plain,
% 0.59/0.63 (~big_p(sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[295, 265, 381, 281, 308, 359, 368])).
% 0.59/0.63 tff(383,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[25, 19, 4, 382, 376])).
% 0.59/0.63 tff(384,plain,(big_r(sk9, sk4(sk9)) | big_p(sk7) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(385,plain,
% 0.59/0.63 (big_r(sk9, sk4(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[384, 5, 4])).
% 0.59/0.63 tff(386,assumption,(~big_r(sk4(sk9), sk3(sk9))), introduced(assumption)).
% 0.59/0.63 tff(387,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(388,plain,
% 0.59/0.63 ((big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))) <=> (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(389,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[388])).
% 0.59/0.63 tff(390,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[389, 387])).
% 0.59/0.63 tff(391,plain,
% 0.59/0.63 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(392,plain,
% 0.59/0.63 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.59/0.63 tff(393,plain,
% 0.59/0.63 (big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[392, 70, 5])).
% 0.59/0.63 tff(394,plain,
% 0.59/0.63 (big_p(sk1(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[393, 386])).
% 0.59/0.63 tff(395,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(396,plain,
% 0.59/0.63 ((big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(397,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[396])).
% 0.59/0.63 tff(398,plain,
% 0.59/0.63 (((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))) <=> ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[397, 395])).
% 0.59/0.63 tff(399,plain,
% 0.59/0.63 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | (big_p(sk9) | big_p(sk7) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(400,plain,
% 0.59/0.63 ((~![E: $i, F: $i] : (big_p(E) | big_p(F) | big_r(sk4(E), sk3(E)) | big_p(sk1(F)))) | big_p(sk9) | big_p(sk7) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.59/0.63 tff(401,plain,
% 0.59/0.63 (big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[400, 70, 5, 4])).
% 0.59/0.63 tff(402,plain,
% 0.59/0.63 (big_p(sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[401, 386])).
% 0.59/0.63 tff(403,assumption,(~big_r(sk2(sk7), sk1(sk7))), introduced(assumption)).
% 0.59/0.63 tff(404,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (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(E1) | big_p(F1))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(405,plain,
% 0.59/0.63 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7)) <=> (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(406,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[405])).
% 0.59/0.63 tff(407,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[406, 404])).
% 0.59/0.63 tff(408,plain,
% 0.59/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7)) | big_p(sk7) | big_p(sk7))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(409,plain,
% 0.59/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.59/0.63 tff(410,plain,
% 0.59/0.63 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[409, 113, 4])).
% 0.59/0.63 tff(411,plain,
% 0.59/0.63 (big_p(sk3(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[410, 403])).
% 0.59/0.63 tff(412,plain,
% 0.59/0.63 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(413,plain,
% 0.59/0.63 ((big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(414,plain,
% 0.59/0.63 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[413])).
% 0.59/0.63 tff(415,plain,
% 0.59/0.63 (((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))) <=> ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[414, 412])).
% 0.59/0.63 tff(416,plain,
% 0.59/0.63 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | (big_p(sk7) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(417,plain,
% 0.59/0.63 ((~![J1: $i, I1: $i] : (big_p(J1) | big_p(I1) | big_r(sk4(I1), sk3(I1)) | big_r(sk2(J1), sk1(J1)))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.59/0.63 tff(418,plain,
% 0.59/0.63 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[417, 161, 5, 4])).
% 0.59/0.63 tff(419,plain,
% 0.59/0.63 (big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[418, 403])).
% 0.59/0.63 tff(420,plain,
% 0.59/0.63 (~big_p(sk3(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[271, 265, 326, 299, 419, 385, 411])).
% 0.59/0.63 tff(421,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | 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(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(422,plain,
% 0.59/0.63 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk7)) <=> (big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(423,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[422])).
% 0.59/0.63 tff(424,plain,
% 0.59/0.63 (((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk7))) <=> ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)))),
% 0.59/0.63 inference(transitivity,[status(thm)],[423, 421])).
% 0.59/0.63 tff(425,plain,
% 0.59/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | big_p(sk7))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(426,plain,
% 0.59/0.63 ((~![E1: $i, F1: $i] : (big_r(sk2(F1), sk1(F1)) | big_p(sk3(E1)) | big_p(E1) | big_p(F1))) | big_p(sk9) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.59/0.63 tff(427,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[426, 113, 5, 4, 403, 420])).
% 0.59/0.63 tff(428,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(429,plain,
% 0.59/0.63 (big_r(sk2(sk7), sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[428, 5, 4])).
% 0.59/0.63 tff(430,plain,
% 0.59/0.63 ((~big_p(sk1(sk7))) | (~big_p(sk1(sk9)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[295, 265, 429, 281, 308, 359])).
% 0.59/0.63 tff(431,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[430, 402, 394])).
% 0.59/0.63 tff(432,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(433,plain,
% 0.59/0.63 (big_r(sk4(sk9), sk3(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[432, 5, 4])).
% 0.59/0.63 tff(434,plain,
% 0.59/0.63 ((~big_p(sk3(sk7))) | (~big_p(sk3(sk9)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[271, 265, 326, 299, 433, 385])).
% 0.59/0.63 tff(435,plain,
% 0.59/0.63 ($false),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[434, 35, 27])).
% 0.59/0.63 tff(436,plain,(big_p(sk1(sk7)) | big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.63 tff(437,plain,
% 0.59/0.63 (big_p(sk1(sk7))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[436, 5, 4])).
% 0.59/0.63 tff(438,plain,
% 0.59/0.63 (~big_p(sk1(sk9))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[430, 437])).
% 0.59/0.63 tff(439,plain,
% 0.59/0.63 (((~![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(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))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(440,plain,
% 0.59/0.64 (((~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))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(441,plain,
% 0.59/0.64 (((~![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)))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[440])).
% 0.59/0.64 tff(442,plain,
% 0.59/0.64 (((~![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))))),
% 0.59/0.64 inference(transitivity,[status(thm)],[441, 439])).
% 0.59/0.64 tff(443,plain,
% 0.59/0.64 ((~![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))))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(444,plain,
% 0.59/0.64 ((~![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)))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.59/0.64 tff(445,plain,
% 0.59/0.64 ((~big_p(sk1(sk7))) | (~big_p(sk3(sk9)))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[444, 265, 429, 281, 433, 385])).
% 0.59/0.64 tff(446,plain,
% 0.59/0.64 (~big_p(sk3(sk9))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[445, 437])).
% 0.59/0.64 tff(447,plain,
% 0.59/0.64 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9)))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(448,plain,
% 0.59/0.64 ((big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9)) <=> (big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(449,plain,
% 0.59/0.64 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[448])).
% 0.59/0.64 tff(450,plain,
% 0.62/0.64 (((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))) <=> ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9)))),
% 0.62/0.64 inference(transitivity,[status(thm)],[449, 447])).
% 0.62/0.64 tff(451,plain,
% 0.62/0.64 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | (big_p(sk3(sk9)) | big_p(sk1(sk9)) | big_p(sk9) | big_p(sk9))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(452,plain,
% 0.62/0.64 ((~![B: $i, A: $i] : (big_p(sk3(A)) | big_p(sk1(B)) | big_p(B) | big_p(A))) | big_p(sk9) | big_p(sk3(sk9)) | big_p(sk1(sk9))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.62/0.64 tff(453,plain,
% 0.62/0.64 (big_p(sk3(sk9)) | big_p(sk1(sk9))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[452, 19, 5])).
% 0.62/0.64 tff(454,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[453, 446, 438])).
% 0.62/0.64 tff(455,plain,(big_p(sk9) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(456,plain,
% 0.62/0.64 (big_p(sk9)),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[455, 4])).
% 0.62/0.64 tff(457,assumption,(~big_r(sk9, sk10)), introduced(assumption)).
% 0.62/0.64 tff(458,plain,
% 0.62/0.64 (big_r(sk7, sk2(sk7)) | big_p(sk3(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[238, 232, 4])).
% 0.62/0.64 tff(459,plain,
% 0.62/0.64 (big_p(sk3(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[458, 211])).
% 0.62/0.64 tff(460,plain,
% 0.62/0.64 (big_r(sk7, sk2(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[254, 57])).
% 0.62/0.64 tff(461,plain,
% 0.62/0.64 (^[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))))),
% 0.62/0.64 inference(bind,[status(th)],[])).
% 0.62/0.64 tff(462,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(quant_intro,[status(thm)],[461])).
% 0.62/0.64 tff(463,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(464,plain,
% 0.62/0.64 (^[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)))))),
% 0.62/0.64 inference(bind,[status(th)],[])).
% 0.62/0.64 tff(465,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(quant_intro,[status(thm)],[464])).
% 0.62/0.64 tff(466,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/sandbox/benchmark/theBenchmark.p','pel38_45')).
% 0.62/0.64 tff(467,plain,
% 0.62/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.62/0.64 tff(468,plain,
% 0.62/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[467, 463])).
% 0.62/0.64 tff(469,plain,(
% 0.62/0.64 ![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.62/0.64 inference(skolemize,[status(sab)],[468])).
% 0.62/0.64 tff(470,plain,
% 0.62/0.64 (![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[469, 462])).
% 0.62/0.64 tff(471,plain,
% 0.62/0.64 (((~![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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(472,plain,
% 0.62/0.64 (((~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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(473,plain,
% 0.62/0.64 (((~![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)))))),
% 0.62/0.64 inference(monotonicity,[status(thm)],[472])).
% 0.62/0.64 tff(474,plain,
% 0.62/0.64 (((~![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))))),
% 0.62/0.64 inference(transitivity,[status(thm)],[473, 471])).
% 0.62/0.64 tff(475,plain,
% 0.62/0.64 ((~![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))))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(476,plain,
% 0.62/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.62/0.64 tff(477,plain,
% 0.62/0.64 (~big_p(sk1(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[476, 456, 457, 470, 316, 460])).
% 0.62/0.64 tff(478,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[323, 70, 4, 57, 477])).
% 0.62/0.64 tff(479,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(480,plain,
% 0.62/0.64 (big_r(sk4(sk7), sk3(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[479, 4, 457])).
% 0.62/0.64 tff(481,plain,
% 0.62/0.64 (((~![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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(482,plain,
% 0.62/0.64 (((~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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(483,plain,
% 0.62/0.64 (((~![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)))))),
% 0.62/0.64 inference(monotonicity,[status(thm)],[482])).
% 0.62/0.64 tff(484,plain,
% 0.62/0.64 (((~![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))))),
% 0.62/0.64 inference(transitivity,[status(thm)],[483, 481])).
% 0.62/0.64 tff(485,plain,
% 0.62/0.64 ((~![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))))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(486,plain,
% 0.62/0.64 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.62/0.64 tff(487,plain,
% 0.62/0.64 ((~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[486, 456, 457, 470, 480])).
% 0.62/0.64 tff(488,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[487, 459, 247])).
% 0.62/0.64 tff(489,plain,(big_r(sk7, sk2(sk7)) | big_r(sk9, sk10) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(490,plain,
% 0.62/0.64 (big_r(sk7, sk2(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[489, 4, 457])).
% 0.62/0.64 tff(491,plain,
% 0.62/0.64 (~big_p(sk1(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[476, 456, 457, 470, 289, 490])).
% 0.62/0.64 tff(492,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[189, 183, 4, 170, 491])).
% 0.62/0.64 tff(493,plain,(big_r(sk7, sk4(sk7)) | big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(494,plain,
% 0.62/0.64 (big_r(sk7, sk4(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[493, 4, 457])).
% 0.62/0.64 tff(495,plain,
% 0.62/0.64 (~big_p(sk3(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[487, 494])).
% 0.62/0.64 tff(496,plain,
% 0.62/0.64 (big_r(sk2(sk7), sk1(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[410, 495])).
% 0.62/0.64 tff(497,plain,
% 0.62/0.64 (~big_p(sk1(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[476, 456, 457, 470, 496, 490])).
% 0.62/0.64 tff(498,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[25, 19, 4, 497, 495])).
% 0.62/0.64 tff(499,plain,(big_p(sk7) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(500,plain,
% 0.62/0.64 (big_r(sk9, sk10)),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[499, 4])).
% 0.62/0.64 tff(501,assumption,(big_p(sk9)), introduced(assumption)).
% 0.62/0.64 tff(502,assumption,(~big_p(sk10)), introduced(assumption)).
% 0.62/0.64 tff(503,plain,
% 0.62/0.64 (big_r(sk7, sk4(sk7))),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[288, 403])).
% 0.62/0.64 tff(504,plain,
% 0.62/0.64 (^[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))))),
% 0.62/0.64 inference(bind,[status(th)],[])).
% 0.62/0.64 tff(505,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(quant_intro,[status(thm)],[504])).
% 0.62/0.64 tff(506,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(507,plain,
% 0.62/0.64 (^[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)))))),
% 0.62/0.64 inference(bind,[status(th)],[])).
% 0.62/0.64 tff(508,plain,
% 0.62/0.64 (![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)))),
% 0.62/0.64 inference(quant_intro,[status(thm)],[507])).
% 0.62/0.64 tff(509,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/sandbox/benchmark/theBenchmark.p','pel38_44')).
% 0.62/0.64 tff(510,plain,
% 0.62/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.62/0.64 tff(511,plain,
% 0.62/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.62/0.64 tff(512,plain,(
% 0.62/0.64 ![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.62/0.64 inference(skolemize,[status(sab)],[511])).
% 0.62/0.64 tff(513,plain,
% 0.62/0.64 (![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[512, 505])).
% 0.62/0.64 tff(514,plain,
% 0.62/0.64 (((~![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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(515,plain,
% 0.62/0.64 ((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))))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(516,plain,
% 0.62/0.64 (((~![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)))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[515])).
% 0.62/0.65 tff(517,plain,
% 0.62/0.65 (((~![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))))),
% 0.62/0.65 inference(transitivity,[status(thm)],[516, 514])).
% 0.62/0.65 tff(518,plain,
% 0.62/0.65 ((~![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))))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(519,plain,
% 0.62/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.62/0.65 tff(520,plain,
% 0.62/0.65 (~big_p(sk3(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[519, 502, 501, 513, 247, 255])).
% 0.62/0.65 tff(521,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[238, 232, 4, 211, 520])).
% 0.62/0.65 tff(522,plain,(big_r(sk7, sk2(sk7)) | big_p(sk7) | big_p(sk10) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.65 tff(523,plain,
% 0.62/0.65 (big_r(sk7, sk2(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[522, 502, 4, 501])).
% 0.62/0.65 tff(524,plain,
% 0.62/0.65 (((~![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))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(525,plain,
% 0.62/0.65 ((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))))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(526,plain,
% 0.62/0.65 (((~![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)))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[525])).
% 0.62/0.65 tff(527,plain,
% 0.62/0.65 (((~![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))))),
% 0.62/0.65 inference(transitivity,[status(thm)],[526, 524])).
% 0.62/0.65 tff(528,plain,
% 0.62/0.65 ((~![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))))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(529,plain,
% 0.62/0.65 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk1(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.62/0.65 tff(530,plain,
% 0.62/0.65 (~big_p(sk1(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[529, 502, 501, 513, 523, 316])).
% 0.62/0.65 tff(531,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[323, 70, 4, 57, 530])).
% 0.62/0.65 tff(532,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | big_p(sk10) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.65 tff(533,plain,
% 0.62/0.65 (big_r(sk4(sk7), sk3(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[532, 502, 4, 501])).
% 0.62/0.65 tff(534,plain,
% 0.62/0.65 ((~big_p(sk3(sk7))) | (~big_r(sk7, sk4(sk7)))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[519, 502, 501, 513, 533])).
% 0.62/0.65 tff(535,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[534, 411, 503])).
% 0.62/0.65 tff(536,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk10) | (~big_p(sk9)) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.65 tff(537,plain,
% 0.62/0.65 (big_r(sk2(sk7), sk1(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[536, 502, 501, 4])).
% 0.62/0.65 tff(538,plain,
% 0.62/0.65 (~big_p(sk1(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[529, 502, 501, 513, 523, 537])).
% 0.62/0.65 tff(539,plain,
% 0.62/0.65 (big_p(sk3(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[25, 19, 4, 538])).
% 0.62/0.65 tff(540,plain,
% 0.62/0.65 (big_r(sk7, sk4(sk7))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[189, 183, 4, 538])).
% 0.62/0.65 tff(541,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[534, 540, 539])).
% 0.62/0.65 tff(542,plain,(big_p(sk10) | (~big_p(sk9)) | big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.65 tff(543,plain,
% 0.62/0.65 (big_p(sk10)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[542, 4, 501])).
% 0.62/0.65 tff(544,assumption,(big_r(sk9, sk10)), introduced(assumption)).
% 0.62/0.65 tff(545,assumption,(big_p(sk10)), introduced(assumption)).
% 0.62/0.65 tff(546,plain,
% 0.62/0.65 (^[O: $i, N: $i, M: $i] : refl((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_r(N, O)) | (~big_p(O)) | big_p(sk5(N))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(547,plain,
% 0.62/0.65 (![O: $i, N: $i, M: $i] : (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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[546])).
% 0.62/0.65 tff(548,plain,
% 0.62/0.65 (![O: $i, N: $i, M: $i] : (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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(549,plain,
% 0.62/0.65 (^[O: $i, N: $i, M: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))) <=> ($false | big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N))))), rewrite(($false | 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_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))) <=> (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(550,plain,
% 0.62/0.65 (![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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[549])).
% 0.62/0.65 tff(551,plain,
% 0.62/0.65 (^[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)))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(552,plain,
% 0.62/0.65 (![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)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[551])).
% 0.62/0.65 tff(553,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/sandbox/benchmark/theBenchmark.p','pel38_7')).
% 0.62/0.65 tff(554,plain,
% 0.62/0.65 (![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)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.62/0.65 tff(555,plain,
% 0.62/0.65 (![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[554, 550])).
% 0.62/0.65 tff(556,plain,
% 0.62/0.65 (![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[555, 548])).
% 0.62/0.65 tff(557,plain,(
% 0.62/0.65 ![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(skolemize,[status(sab)],[556])).
% 0.62/0.65 tff(558,plain,
% 0.62/0.65 (![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[557, 547])).
% 0.62/0.65 tff(559,plain,
% 0.62/0.65 (((~![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(560,plain,
% 0.62/0.65 ((big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9))) <=> (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(561,plain,
% 0.62/0.65 (((~![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[560])).
% 0.62/0.65 tff(562,plain,
% 0.62/0.65 (((~![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (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(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[561, 559])).
% 0.62/0.65 tff(563,plain,
% 0.62/0.65 ((~![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | (big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_p(sk5(sk9)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(564,plain,
% 0.62/0.65 ((~![O: $i, N: $i, M: $i] : (big_p(M) | big_p(sk1(M)) | (~big_r(N, O)) | (~big_p(O)) | big_p(sk5(N)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.62/0.65 tff(565,plain,
% 0.62/0.65 (big_p(sk1(sk7)) | big_p(sk5(sk9))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[564, 558, 545, 4, 544])).
% 0.62/0.65 tff(566,plain,
% 0.62/0.65 (big_p(sk5(sk9))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[565, 6])).
% 0.62/0.65 tff(567,plain,
% 0.62/0.65 (^[R: $i, Q: $i, P: $i] : refl((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, R)) | (~big_p(R)) | big_r(Q, sk6(Q))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(568,plain,
% 0.62/0.65 (![R: $i, Q: $i, P: $i] : (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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[567])).
% 0.62/0.65 tff(569,plain,
% 0.62/0.65 (![R: $i, Q: $i, P: $i] : (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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(570,plain,
% 0.62/0.65 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))) <=> ($false | big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q))))), rewrite(($false | 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, 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))) <=> (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(571,plain,
% 0.62/0.65 (![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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[570])).
% 0.62/0.65 tff(572,plain,
% 0.62/0.65 (^[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)))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(573,plain,
% 0.62/0.65 (![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)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[572])).
% 0.62/0.65 tff(574,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/sandbox/benchmark/theBenchmark.p','pel38_8')).
% 0.62/0.65 tff(575,plain,
% 0.62/0.65 (![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)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.62/0.65 tff(576,plain,
% 0.62/0.65 (![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[575, 571])).
% 0.62/0.65 tff(577,plain,
% 0.62/0.65 (![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[576, 569])).
% 0.62/0.65 tff(578,plain,(
% 0.62/0.65 ![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(skolemize,[status(sab)],[577])).
% 0.62/0.65 tff(579,plain,
% 0.62/0.65 (![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[578, 568])).
% 0.62/0.65 tff(580,plain,
% 0.62/0.65 (((~![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(581,plain,
% 0.62/0.65 ((big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))) <=> (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(582,plain,
% 0.62/0.65 (((~![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[581])).
% 0.62/0.65 tff(583,plain,
% 0.62/0.65 (((~![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (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(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[582, 580])).
% 0.62/0.65 tff(584,plain,
% 0.62/0.65 ((~![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | (big_p(sk7) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(585,plain,
% 0.62/0.65 ((~![R: $i, Q: $i, P: $i] : (big_p(P) | big_p(sk1(P)) | (~big_r(Q, R)) | (~big_p(R)) | big_r(Q, sk6(Q)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.62/0.65 tff(586,plain,
% 0.62/0.65 (big_p(sk1(sk7)) | big_r(sk9, sk6(sk9))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[585, 579, 545, 4, 544])).
% 0.62/0.65 tff(587,plain,
% 0.62/0.65 (big_r(sk9, sk6(sk9))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[586, 6])).
% 0.62/0.65 tff(588,plain,
% 0.62/0.65 (^[S: $i, T: $i, U: $i] : refl((big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(589,plain,
% 0.62/0.65 (![S: $i, T: $i, U: $i] : (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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[588])).
% 0.62/0.65 tff(590,plain,
% 0.62/0.65 (![S: $i, T: $i, U: $i] : (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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(591,plain,
% 0.62/0.65 (^[S: $i, T: $i, U: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> ($false | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))))), rewrite(($false | big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S))) <=> (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))) <=> (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(592,plain,
% 0.62/0.65 (![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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[591])).
% 0.62/0.65 tff(593,plain,
% 0.62/0.65 (^[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)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(594,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[593])).
% 0.62/0.66 tff(595,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/sandbox/benchmark/theBenchmark.p','pel38_9')).
% 0.62/0.66 tff(596,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.62/0.66 tff(597,plain,
% 0.62/0.66 (![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[596, 592])).
% 0.62/0.66 tff(598,plain,
% 0.62/0.66 (![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[597, 590])).
% 0.62/0.66 tff(599,plain,(
% 0.62/0.66 ![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[598])).
% 0.62/0.66 tff(600,plain,
% 0.62/0.66 (![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[599, 589])).
% 0.62/0.66 tff(601,plain,
% 0.62/0.66 (((~![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(602,plain,
% 0.62/0.66 ((big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7))) <=> (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(603,plain,
% 0.62/0.66 (((~![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[602])).
% 0.62/0.66 tff(604,plain,
% 0.62/0.66 (((~![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (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(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[603, 601])).
% 0.62/0.66 tff(605,plain,
% 0.62/0.66 ((~![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | (big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk7)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(606,plain,
% 0.62/0.66 ((~![S: $i, T: $i, U: $i] : (big_p(S) | (~big_r(T, U)) | (~big_p(U)) | big_r(sk6(T), sk5(T)) | big_p(sk1(S)))) | big_p(sk7) | (~big_p(sk10)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.62/0.66 tff(607,plain,
% 0.62/0.66 (big_p(sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[606, 600, 545, 4, 544])).
% 0.62/0.66 tff(608,plain,
% 0.62/0.66 (big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[607, 6])).
% 0.62/0.66 tff(609,plain,
% 0.62/0.66 (^[D2: $i, E2: $i, C2: $i] : refl((big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(610,plain,
% 0.62/0.66 (![D2: $i, E2: $i, C2: $i] : (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[609])).
% 0.62/0.66 tff(611,plain,
% 0.62/0.66 (![D2: $i, E2: $i, C2: $i] : (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(612,plain,
% 0.62/0.66 (^[D2: $i, E2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> ($false | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))))), rewrite(($false | big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2))) <=> (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))) <=> (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(613,plain,
% 0.62/0.66 (![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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[612])).
% 0.62/0.66 tff(614,plain,
% 0.62/0.66 (^[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)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(615,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[614])).
% 0.62/0.66 tff(616,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/sandbox/benchmark/theBenchmark.p','pel38_22')).
% 0.62/0.66 tff(617,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.62/0.66 tff(618,plain,
% 0.62/0.66 (![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[617, 613])).
% 0.62/0.66 tff(619,plain,
% 0.62/0.66 (![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[618, 611])).
% 0.62/0.66 tff(620,plain,(
% 0.62/0.66 ![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[619])).
% 0.62/0.66 tff(621,plain,
% 0.62/0.66 (![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[620, 610])).
% 0.62/0.66 tff(622,plain,
% 0.62/0.66 (((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(623,plain,
% 0.62/0.66 ((big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(624,plain,
% 0.62/0.66 (((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[623])).
% 0.62/0.66 tff(625,plain,
% 0.62/0.66 (((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[624, 622])).
% 0.62/0.66 tff(626,plain,
% 0.62/0.66 ((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(627,plain,
% 0.62/0.66 ((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.62/0.66 tff(628,plain,
% 0.62/0.66 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_p(sk1(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[627, 621, 4, 544])).
% 0.62/0.66 tff(629,plain,
% 0.62/0.66 (big_p(sk1(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[628, 57, 545])).
% 0.62/0.66 tff(630,plain,
% 0.62/0.66 (^[K2: $i, I2: $i, J2: $i] : refl((big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))) <=> (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(631,plain,
% 0.62/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[630])).
% 0.62/0.66 tff(632,plain,
% 0.62/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(633,plain,
% 0.62/0.66 (^[K2: $i, I2: $i, J2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), ((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)) | $false | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))))), rewrite((big_r(sk2(J2), sk1(J2)) | $false | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2))) <=> (big_r(sk2(J2), sk1(J2)) | 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_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(634,plain,
% 0.62/0.66 (![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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[633])).
% 0.62/0.66 tff(635,plain,
% 0.62/0.66 (^[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)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(636,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[635])).
% 0.62/0.66 tff(637,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/sandbox/benchmark/theBenchmark.p','pel38_24')).
% 0.62/0.66 tff(638,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.62/0.66 tff(639,plain,
% 0.62/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[638, 634])).
% 0.62/0.66 tff(640,plain,
% 0.62/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[639, 632])).
% 0.62/0.66 tff(641,plain,(
% 0.62/0.66 ![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[640])).
% 0.62/0.66 tff(642,plain,
% 0.62/0.66 (![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[641, 631])).
% 0.62/0.66 tff(643,plain,
% 0.62/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(644,plain,
% 0.62/0.66 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(645,plain,
% 0.62/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[644])).
% 0.62/0.66 tff(646,plain,
% 0.62/0.66 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[645, 643])).
% 0.62/0.66 tff(647,plain,
% 0.62/0.66 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(648,plain,
% 0.62/0.66 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.62/0.66 tff(649,plain,
% 0.62/0.66 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[648, 642, 4, 544])).
% 0.62/0.66 tff(650,plain,
% 0.62/0.66 (big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[649, 57, 545])).
% 0.62/0.66 tff(651,plain,
% 0.62/0.66 (^[G2: $i, H2: $i, F2: $i] : refl((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(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(652,plain,
% 0.62/0.66 (![G2: $i, H2: $i, F2: $i] : (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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[651])).
% 0.62/0.66 tff(653,plain,
% 0.62/0.66 (![G2: $i, H2: $i, F2: $i] : (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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(654,plain,
% 0.62/0.66 (^[G2: $i, H2: $i, F2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))) <=> ($false | big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2))))), rewrite(($false | 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(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))) <=> (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(655,plain,
% 0.62/0.66 (![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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[654])).
% 0.62/0.66 tff(656,plain,
% 0.62/0.66 (^[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)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(657,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[656])).
% 0.62/0.66 tff(658,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/sandbox/benchmark/theBenchmark.p','pel38_23')).
% 0.62/0.66 tff(659,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.62/0.66 tff(660,plain,
% 0.62/0.66 (![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[659, 655])).
% 0.62/0.66 tff(661,plain,
% 0.62/0.66 (![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[660, 653])).
% 0.62/0.66 tff(662,plain,(
% 0.62/0.66 ![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[661])).
% 0.62/0.66 tff(663,plain,
% 0.62/0.66 (![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[662, 652])).
% 0.62/0.66 tff(664,plain,
% 0.62/0.66 (((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(665,plain,
% 0.62/0.66 ((big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))) <=> (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(666,plain,
% 0.62/0.66 (((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[665])).
% 0.62/0.66 tff(667,plain,
% 0.62/0.66 (((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[666, 664])).
% 0.62/0.67 tff(668,plain,
% 0.62/0.67 ((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(669,plain,
% 0.62/0.67 ((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk7) | big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.62/0.67 tff(670,plain,
% 0.62/0.67 (big_r(sk4(sk7), sk3(sk7)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[669, 663, 4, 544])).
% 0.62/0.67 tff(671,plain,
% 0.62/0.67 (big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[670, 57, 545])).
% 0.62/0.67 tff(672,plain,
% 0.62/0.67 (~big_p(sk1(sk7))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[295, 265, 460, 316, 671, 650, 629])).
% 0.62/0.67 tff(673,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[323, 70, 4, 57, 672])).
% 0.62/0.67 tff(674,plain,(big_r(sk4(sk7), sk3(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(675,plain,
% 0.62/0.67 (big_r(sk4(sk7), sk3(sk7))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[674, 4, 545, 544])).
% 0.62/0.67 tff(676,plain,
% 0.62/0.67 (^[R1: $i, S1: $i, Q1: $i] : refl((big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(677,plain,
% 0.62/0.67 (![R1: $i, S1: $i, Q1: $i] : (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[676])).
% 0.62/0.67 tff(678,plain,
% 0.62/0.67 (![R1: $i, S1: $i, Q1: $i] : (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(679,plain,
% 0.62/0.67 (^[R1: $i, S1: $i, Q1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> ($false | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))))), rewrite(($false | big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1))) <=> (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))) <=> (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(680,plain,
% 0.62/0.67 (![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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[679])).
% 0.62/0.67 tff(681,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(682,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[681])).
% 0.62/0.67 tff(683,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/sandbox/benchmark/theBenchmark.p','pel38_18')).
% 0.62/0.67 tff(684,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.62/0.67 tff(685,plain,
% 0.62/0.67 (![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[684, 680])).
% 0.62/0.67 tff(686,plain,
% 0.62/0.67 (![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[685, 678])).
% 0.62/0.67 tff(687,plain,(
% 0.62/0.67 ![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(skolemize,[status(sab)],[686])).
% 0.62/0.67 tff(688,plain,
% 0.62/0.67 (![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[687, 677])).
% 0.62/0.67 tff(689,plain,
% 0.62/0.67 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(690,plain,
% 0.62/0.67 ((big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(691,plain,
% 0.62/0.67 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[690])).
% 0.62/0.67 tff(692,plain,
% 0.62/0.67 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[691, 689])).
% 0.62/0.67 tff(693,plain,
% 0.62/0.67 ((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(694,plain,
% 0.62/0.67 ((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.62/0.67 tff(695,plain,
% 0.62/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_p(sk1(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[694, 688, 4, 544])).
% 0.62/0.67 tff(696,plain,
% 0.62/0.67 (big_p(sk1(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[695, 170, 545])).
% 0.62/0.67 tff(697,plain,
% 0.62/0.67 (big_r(sk7, sk4(sk7)) | big_p(sk1(sk7))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[189, 183, 4])).
% 0.62/0.67 tff(698,plain,
% 0.62/0.67 (big_p(sk1(sk7))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[697, 170])).
% 0.62/0.67 tff(699,plain,
% 0.62/0.67 (^[A2: $i, B2: $i, Z1: $i] : refl((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(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(700,plain,
% 0.62/0.67 (![A2: $i, B2: $i, Z1: $i] : (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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[699])).
% 0.62/0.67 tff(701,plain,
% 0.62/0.67 (![A2: $i, B2: $i, Z1: $i] : (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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(702,plain,
% 0.62/0.67 (^[A2: $i, B2: $i, Z1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))) <=> ($false | big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2))))), rewrite(($false | 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(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))) <=> (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(703,plain,
% 0.62/0.67 (![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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[702])).
% 0.62/0.67 tff(704,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(705,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[704])).
% 0.62/0.67 tff(706,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/sandbox/benchmark/theBenchmark.p','pel38_21')).
% 0.62/0.67 tff(707,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.62/0.67 tff(708,plain,
% 0.62/0.67 (![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[707, 703])).
% 0.62/0.67 tff(709,plain,
% 0.62/0.67 (![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[708, 701])).
% 0.62/0.67 tff(710,plain,(
% 0.62/0.67 ![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(skolemize,[status(sab)],[709])).
% 0.62/0.67 tff(711,plain,
% 0.62/0.67 (![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[710, 700])).
% 0.62/0.67 tff(712,plain,
% 0.62/0.67 (((~![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(713,plain,
% 0.62/0.67 ((big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))) <=> (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(714,plain,
% 0.62/0.67 (((~![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[713])).
% 0.62/0.67 tff(715,plain,
% 0.62/0.67 (((~![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[714, 712])).
% 0.62/0.67 tff(716,plain,
% 0.62/0.67 ((~![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(717,plain,
% 0.62/0.67 ((~![A2: $i, B2: $i, Z1: $i] : (big_p(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.62/0.67 tff(718,plain,
% 0.62/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[717, 711, 4, 544])).
% 0.62/0.67 tff(719,plain,
% 0.62/0.67 (big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[718, 170, 545])).
% 0.62/0.67 tff(720,plain,
% 0.62/0.67 (^[V1: $i, T1: $i, U1: $i] : refl((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(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(721,plain,
% 0.62/0.67 (![V1: $i, T1: $i, U1: $i] : (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[720])).
% 0.62/0.67 tff(722,plain,
% 0.62/0.67 (![V1: $i, T1: $i, U1: $i] : (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(723,plain,
% 0.62/0.67 (^[V1: $i, T1: $i, U1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))) <=> ($false | big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1))))), rewrite(($false | 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(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(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(724,plain,
% 0.62/0.67 (![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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[723])).
% 0.62/0.67 tff(725,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(726,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[725])).
% 0.62/0.67 tff(727,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/sandbox/benchmark/theBenchmark.p','pel38_19')).
% 0.62/0.67 tff(728,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.62/0.67 tff(729,plain,
% 0.62/0.67 (![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.62/0.67 tff(730,plain,
% 0.62/0.67 (![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[729, 722])).
% 0.62/0.67 tff(731,plain,(
% 0.62/0.67 ![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(skolemize,[status(sab)],[730])).
% 0.62/0.67 tff(732,plain,
% 0.62/0.67 (![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[731, 721])).
% 0.62/0.67 tff(733,plain,
% 0.62/0.67 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(734,plain,
% 0.62/0.67 ((big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(735,plain,
% 0.62/0.67 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[734])).
% 0.62/0.67 tff(736,plain,
% 0.62/0.67 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[735, 733])).
% 0.62/0.67 tff(737,plain,
% 0.62/0.67 ((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk7) | big_r(sk9, sk2(sk9)) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(738,plain,
% 0.62/0.67 ((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk7) | big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.62/0.67 tff(739,plain,
% 0.62/0.67 (big_r(sk7, sk4(sk7)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[738, 732, 4, 544])).
% 0.62/0.67 tff(740,plain,
% 0.62/0.67 (big_r(sk9, sk2(sk9))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[739, 170, 545])).
% 0.62/0.67 tff(741,plain,
% 0.62/0.67 (^[M2: $i, L2: $i, N2: $i] : refl((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(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(742,plain,
% 0.62/0.67 (![M2: $i, L2: $i, N2: $i] : (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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[741])).
% 0.62/0.67 tff(743,plain,
% 0.62/0.67 (![M2: $i, L2: $i, N2: $i] : (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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(744,plain,
% 0.62/0.67 (^[M2: $i, L2: $i, N2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))) <=> ($false | big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2))))), rewrite(($false | 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(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))) <=> (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(745,plain,
% 0.62/0.67 (![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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[744])).
% 0.62/0.67 tff(746,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(747,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[746])).
% 0.62/0.68 tff(748,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/sandbox/benchmark/theBenchmark.p','pel38_25')).
% 0.62/0.68 tff(749,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.62/0.68 tff(750,plain,
% 0.62/0.68 (![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[749, 745])).
% 0.62/0.68 tff(751,plain,
% 0.62/0.68 (![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[750, 743])).
% 0.62/0.68 tff(752,plain,(
% 0.62/0.68 ![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[751])).
% 0.62/0.68 tff(753,plain,
% 0.62/0.68 (![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[752, 742])).
% 0.62/0.68 tff(754,plain,
% 0.62/0.68 (((~![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(755,plain,
% 0.62/0.68 ((big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(756,plain,
% 0.62/0.68 (((~![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[755])).
% 0.62/0.68 tff(757,plain,
% 0.62/0.68 (((~![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (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(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[756, 754])).
% 0.62/0.68 tff(758,plain,
% 0.62/0.68 ((~![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | (big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(759,plain,
% 0.62/0.68 ((~![M2: $i, L2: $i, N2: $i] : (big_p(L2) | (~big_p(N2)) | (~big_r(M2, N2)) | big_p(sk5(M2)) | big_r(sk2(L2), sk1(L2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.62/0.68 tff(760,plain,
% 0.62/0.68 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[759, 753, 4, 544])).
% 0.62/0.68 tff(761,plain,
% 0.62/0.68 (big_p(sk5(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[760, 403, 545])).
% 0.62/0.68 tff(762,plain,
% 0.62/0.68 (^[O2: $i, P2: $i, Q2: $i] : refl((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(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(763,plain,
% 0.62/0.68 (![O2: $i, P2: $i, Q2: $i] : (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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[762])).
% 0.62/0.68 tff(764,plain,
% 0.62/0.68 (![O2: $i, P2: $i, Q2: $i] : (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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(765,plain,
% 0.62/0.68 (^[O2: $i, P2: $i, Q2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))) <=> ($false | big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2))))), rewrite(($false | 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(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))) <=> (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(766,plain,
% 0.62/0.68 (![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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[765])).
% 0.62/0.68 tff(767,plain,
% 0.62/0.68 (^[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)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(768,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[767])).
% 0.62/0.68 tff(769,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/sandbox/benchmark/theBenchmark.p','pel38_26')).
% 0.62/0.68 tff(770,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.62/0.68 tff(771,plain,
% 0.62/0.68 (![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.62/0.68 tff(772,plain,
% 0.62/0.68 (![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[771, 764])).
% 0.62/0.68 tff(773,plain,(
% 0.62/0.68 ![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[772])).
% 0.62/0.68 tff(774,plain,
% 0.62/0.68 (![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[773, 763])).
% 0.62/0.68 tff(775,plain,
% 0.62/0.68 (((~![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(776,plain,
% 0.62/0.68 ((big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7))) <=> (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(777,plain,
% 0.62/0.68 (((~![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[776])).
% 0.62/0.68 tff(778,plain,
% 0.62/0.68 (((~![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[777, 775])).
% 0.62/0.68 tff(779,plain,
% 0.62/0.68 ((~![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (big_p(sk7) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(780,plain,
% 0.62/0.68 ((~![O2: $i, P2: $i, Q2: $i] : (big_p(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.62/0.68 tff(781,plain,
% 0.62/0.68 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[780, 774, 4, 544])).
% 0.62/0.68 tff(782,plain,
% 0.62/0.68 (big_r(sk9, sk6(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[781, 403, 545])).
% 0.62/0.68 tff(783,plain,
% 0.62/0.68 (^[T2: $i, S2: $i, R2: $i] : refl((big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) <=> (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(784,plain,
% 0.62/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[783])).
% 0.62/0.68 tff(785,plain,
% 0.62/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(786,plain,
% 0.62/0.68 (^[T2: $i, S2: $i, R2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), ((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)) | $false | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))))), rewrite((big_r(sk2(R2), sk1(R2)) | $false | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2))) <=> (big_r(sk2(R2), sk1(R2)) | 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))) <=> (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(787,plain,
% 0.62/0.68 (![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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[786])).
% 0.62/0.68 tff(788,plain,
% 0.62/0.68 (^[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)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(789,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[788])).
% 0.62/0.68 tff(790,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/sandbox/benchmark/theBenchmark.p','pel38_27')).
% 0.62/0.68 tff(791,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.62/0.68 tff(792,plain,
% 0.62/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[791, 787])).
% 0.62/0.68 tff(793,plain,
% 0.62/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[792, 785])).
% 0.62/0.68 tff(794,plain,(
% 0.62/0.68 ![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[793])).
% 0.62/0.68 tff(795,plain,
% 0.62/0.68 (![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[794, 784])).
% 0.62/0.68 tff(796,plain,
% 0.62/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(797,plain,
% 0.62/0.68 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))) <=> (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(798,plain,
% 0.62/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[797])).
% 0.62/0.68 tff(799,plain,
% 0.62/0.68 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[798, 796])).
% 0.62/0.68 tff(800,plain,
% 0.62/0.68 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(801,plain,
% 0.62/0.68 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk7) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.62/0.68 tff(802,plain,
% 0.62/0.68 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[801, 795, 545, 4, 544])).
% 0.62/0.68 tff(803,plain,
% 0.62/0.68 (big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[802, 403])).
% 0.62/0.68 tff(804,plain,
% 0.62/0.68 (((~![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))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(805,plain,
% 0.62/0.68 (((~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))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(806,plain,
% 0.62/0.68 (((~![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)))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[805])).
% 0.62/0.69 tff(807,plain,
% 0.62/0.69 (((~![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))))),
% 0.62/0.69 inference(transitivity,[status(thm)],[806, 804])).
% 0.62/0.69 tff(808,plain,
% 0.62/0.69 ((~![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))))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(809,plain,
% 0.62/0.69 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk7))) | (~big_r(sk4(sk7), sk3(sk7))) | (~big_r(sk7, sk4(sk7))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.62/0.69 tff(810,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[809, 265, 503, 675, 803, 782, 761, 411])).
% 0.62/0.69 tff(811,plain,(big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk7) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(812,plain,
% 0.62/0.69 (big_r(sk2(sk7), sk1(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[811, 545, 4, 544])).
% 0.62/0.69 tff(813,plain,
% 0.62/0.69 (^[W: $i, V: $i, X: $i] : refl((big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(814,plain,
% 0.62/0.69 (![W: $i, V: $i, X: $i] : (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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[813])).
% 0.62/0.69 tff(815,plain,
% 0.62/0.69 (![W: $i, V: $i, X: $i] : (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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(816,plain,
% 0.62/0.69 (^[W: $i, V: $i, X: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> ($false | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))))), rewrite(($false | big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W))) <=> (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))) <=> (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(817,plain,
% 0.62/0.69 (![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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[816])).
% 0.62/0.69 tff(818,plain,
% 0.62/0.69 (^[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)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(819,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[818])).
% 0.62/0.69 tff(820,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/sandbox/benchmark/theBenchmark.p','pel38_10')).
% 0.62/0.69 tff(821,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.62/0.69 tff(822,plain,
% 0.62/0.69 (![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[821, 817])).
% 0.62/0.69 tff(823,plain,
% 0.62/0.69 (![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[822, 815])).
% 0.62/0.69 tff(824,plain,(
% 0.62/0.69 ![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[823])).
% 0.62/0.69 tff(825,plain,
% 0.62/0.69 (![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[824, 814])).
% 0.62/0.69 tff(826,plain,
% 0.62/0.69 (((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(827,plain,
% 0.62/0.69 ((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(828,plain,
% 0.62/0.69 ((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.62/0.69 tff(829,plain,
% 0.62/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[828, 825, 4, 544])).
% 0.62/0.69 tff(830,plain,
% 0.62/0.69 (big_p(sk5(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[829, 211, 545])).
% 0.62/0.69 tff(831,plain,
% 0.62/0.69 (^[Z: $i, A1: $i, Y: $i] : refl((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(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(832,plain,
% 0.62/0.69 (![Z: $i, A1: $i, Y: $i] : (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[831])).
% 0.62/0.69 tff(833,plain,
% 0.62/0.69 (![Z: $i, A1: $i, Y: $i] : (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(834,plain,
% 0.62/0.69 (^[Z: $i, A1: $i, Y: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))) <=> ($false | big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z))))), rewrite(($false | 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(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))) <=> (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(835,plain,
% 0.62/0.69 (![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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[834])).
% 0.62/0.69 tff(836,plain,
% 0.62/0.69 (^[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)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(837,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[836])).
% 0.62/0.69 tff(838,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/sandbox/benchmark/theBenchmark.p','pel38_11')).
% 0.62/0.69 tff(839,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.62/0.69 tff(840,plain,
% 0.62/0.69 (![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[839, 835])).
% 0.62/0.69 tff(841,plain,
% 0.62/0.69 (![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[840, 833])).
% 0.62/0.69 tff(842,plain,(
% 0.62/0.69 ![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[841])).
% 0.62/0.69 tff(843,plain,
% 0.62/0.69 (![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[842, 832])).
% 0.62/0.69 tff(844,plain,
% 0.62/0.69 (((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(845,plain,
% 0.62/0.69 ((big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))) <=> (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(846,plain,
% 0.62/0.69 (((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[845])).
% 0.62/0.69 tff(847,plain,
% 0.62/0.69 (((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[846, 844])).
% 0.62/0.69 tff(848,plain,
% 0.62/0.69 ((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(849,plain,
% 0.62/0.69 ((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.62/0.69 tff(850,plain,
% 0.62/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[849, 843, 4, 544])).
% 0.62/0.69 tff(851,plain,
% 0.62/0.69 (big_r(sk9, sk6(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[850, 211, 545])).
% 0.62/0.69 tff(852,plain,
% 0.62/0.69 (^[B1: $i, D1: $i, C1: $i] : refl((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_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(853,plain,
% 0.62/0.69 (![B1: $i, D1: $i, C1: $i] : (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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[852])).
% 0.62/0.69 tff(854,plain,
% 0.62/0.69 (![B1: $i, D1: $i, C1: $i] : (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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(855,plain,
% 0.62/0.69 (^[B1: $i, D1: $i, C1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))) <=> ($false | big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1))))), rewrite(($false | 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_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))) <=> (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(856,plain,
% 0.62/0.69 (![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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[855])).
% 0.62/0.69 tff(857,plain,
% 0.62/0.69 (^[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)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(858,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[857])).
% 0.62/0.69 tff(859,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/sandbox/benchmark/theBenchmark.p','pel38_12')).
% 0.62/0.69 tff(860,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[859, 858])).
% 0.62/0.69 tff(861,plain,
% 0.62/0.69 (![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[860, 856])).
% 0.62/0.69 tff(862,plain,
% 0.62/0.69 (![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[861, 854])).
% 0.62/0.69 tff(863,plain,(
% 0.62/0.69 ![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[862])).
% 0.62/0.69 tff(864,plain,
% 0.62/0.69 (![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[863, 853])).
% 0.62/0.69 tff(865,plain,
% 0.62/0.69 (((~![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(866,plain,
% 0.62/0.69 ((big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7))) <=> (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(867,plain,
% 0.62/0.69 (((~![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[866])).
% 0.62/0.69 tff(868,plain,
% 0.62/0.69 (((~![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (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(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[867, 865])).
% 0.62/0.69 tff(869,plain,
% 0.62/0.69 ((~![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | (big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk2(sk7)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(870,plain,
% 0.62/0.69 ((~![B1: $i, D1: $i, C1: $i] : (big_p(B1) | (~big_p(D1)) | (~big_r(C1, D1)) | big_r(sk6(C1), sk5(C1)) | big_r(B1, sk2(B1)))) | big_p(sk7) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.62/0.69 tff(871,plain,
% 0.62/0.69 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[870, 864, 4, 544])).
% 0.62/0.69 tff(872,plain,
% 0.62/0.69 (big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[871, 211, 545])).
% 0.62/0.69 tff(873,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[809, 265, 247, 675, 872, 851, 830, 459])).
% 0.62/0.69 tff(874,plain,(big_r(sk7, sk2(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(875,plain,
% 0.62/0.69 (big_r(sk7, sk2(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[874, 4, 545, 544])).
% 0.62/0.69 tff(876,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[295, 265, 875, 812, 740, 719, 698, 696])).
% 0.62/0.69 tff(877,plain,(big_r(sk7, sk4(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(878,plain,
% 0.62/0.69 (big_r(sk7, sk4(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[877, 4, 545, 544])).
% 0.62/0.69 tff(879,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[809, 265, 878, 675, 608, 587, 566, 27])).
% 0.62/0.69 tff(880,plain,(big_p(sk1(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(881,plain,
% 0.62/0.69 (big_p(sk1(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[880, 4, 543, 544])).
% 0.62/0.69 tff(882,plain,
% 0.62/0.69 (big_r(sk2(sk7), sk1(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[811, 543, 4, 544])).
% 0.62/0.69 tff(883,plain,
% 0.62/0.69 (big_r(sk7, sk2(sk7))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[874, 4, 543, 544])).
% 0.62/0.69 tff(884,assumption,(~big_r(sk9, sk6(sk9))), introduced(assumption)).
% 0.62/0.69 tff(885,plain,
% 0.62/0.69 (^[E3: $i, F3: $i, D3: $i, C3: $i] : refl((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_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(886,plain,
% 0.62/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[885])).
% 0.62/0.69 tff(887,plain,
% 0.62/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(888,plain,
% 0.62/0.69 (^[E3: $i, F3: $i, D3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))) <=> ($false | big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3))))), rewrite(($false | 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_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))) <=> (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(889,plain,
% 0.62/0.69 (![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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[888])).
% 0.62/0.69 tff(890,plain,
% 0.62/0.69 (^[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)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(891,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[890])).
% 0.62/0.69 tff(892,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/sandbox/benchmark/theBenchmark.p','pel38_30')).
% 0.62/0.69 tff(893,plain,
% 0.62/0.69 (![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)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.62/0.69 tff(894,plain,
% 0.62/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[893, 889])).
% 0.62/0.69 tff(895,plain,
% 0.62/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[894, 887])).
% 0.62/0.69 tff(896,plain,(
% 0.62/0.69 ![E3: $i, F3: $i, D3: $i, C3: $i] : (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[895])).
% 0.62/0.69 tff(897,plain,
% 0.62/0.69 (![E3: $i, F3: $i, D3: $i, C3: $i] : (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[896, 886])).
% 0.62/0.70 tff(898,plain,
% 0.62/0.70 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(899,plain,
% 0.62/0.70 ((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(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(900,plain,
% 0.62/0.70 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[899])).
% 0.62/0.70 tff(901,plain,
% 0.62/0.70 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[900, 898])).
% 0.62/0.70 tff(902,plain,
% 0.62/0.70 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk9)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(903,plain,
% 0.62/0.70 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.62/0.70 tff(904,plain,
% 0.62/0.70 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[903, 897, 544])).
% 0.62/0.70 tff(905,plain,
% 0.62/0.70 (big_p(sk1(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[904, 884, 545])).
% 0.62/0.70 tff(906,assumption,(big_p(sk1(sk7))), introduced(assumption)).
% 0.62/0.70 tff(907,plain,
% 0.62/0.70 (^[O3: $i, P3: $i, R3: $i, Q3: $i] : refl(((~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(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(908,plain,
% 0.62/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[907])).
% 0.62/0.70 tff(909,plain,
% 0.62/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(910,plain,
% 0.62/0.70 (^[O3: $i, P3: $i, R3: $i, Q3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_p(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3))) <=> ($false | (~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))))), rewrite(($false | (~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(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))) <=> ((~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)))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(911,plain,
% 0.62/0.70 (![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(Q3)) | (~big_r(P3, R3)) | (~big_p(R3)) | big_r(sk2(P3), sk1(P3)) | big_r(O3, sk6(O3)) | (~big_r(O3, Q3)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[910])).
% 0.62/0.70 tff(912,plain,
% 0.62/0.70 (^[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)))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(913,plain,
% 0.62/0.70 (![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)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[912])).
% 0.62/0.70 tff(914,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/sandbox/benchmark/theBenchmark.p','pel38_33')).
% 0.62/0.70 tff(915,plain,
% 0.62/0.70 (![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)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.62/0.70 tff(916,plain,
% 0.62/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[915, 911])).
% 0.62/0.70 tff(917,plain,
% 0.62/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[916, 909])).
% 0.62/0.70 tff(918,plain,(
% 0.62/0.70 ![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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)))),
% 0.62/0.70 inference(skolemize,[status(sab)],[917])).
% 0.62/0.70 tff(919,plain,
% 0.62/0.70 (![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[918, 908])).
% 0.62/0.70 tff(920,plain,
% 0.62/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(921,plain,
% 0.62/0.70 (((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(922,plain,
% 0.62/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[921])).
% 0.62/0.70 tff(923,plain,
% 0.62/0.70 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[922, 920])).
% 0.62/0.70 tff(924,plain,
% 0.62/0.70 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(925,plain,
% 0.62/0.70 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.62/0.70 tff(926,plain,
% 0.62/0.70 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[925, 919, 544])).
% 0.62/0.70 tff(927,plain,
% 0.62/0.70 (big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[926, 884, 545])).
% 0.62/0.70 tff(928,plain,
% 0.62/0.70 (^[G3: $i, H3: $i, I3: $i, J3: $i] : refl(((~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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(929,plain,
% 0.62/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[928])).
% 0.62/0.70 tff(930,plain,
% 0.62/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(931,plain,
% 0.62/0.70 (^[G3: $i, H3: $i, I3: $i, J3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))) <=> ($false | (~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3))))), rewrite(($false | (~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(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))) <=> ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(932,plain,
% 0.62/0.70 (![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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[931])).
% 0.62/0.70 tff(933,plain,
% 0.62/0.70 (^[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)))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(934,plain,
% 0.62/0.70 (![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)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[933])).
% 0.62/0.70 tff(935,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/sandbox/benchmark/theBenchmark.p','pel38_31')).
% 0.62/0.70 tff(936,plain,
% 0.62/0.70 (![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)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.62/0.70 tff(937,plain,
% 0.62/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[936, 932])).
% 0.62/0.70 tff(938,plain,
% 0.62/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[937, 930])).
% 0.62/0.70 tff(939,plain,(
% 0.62/0.70 ![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(skolemize,[status(sab)],[938])).
% 0.62/0.70 tff(940,plain,
% 0.62/0.70 (![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[939, 929])).
% 0.62/0.70 tff(941,plain,
% 0.62/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(942,plain,
% 0.62/0.70 (((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(943,plain,
% 0.62/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[942])).
% 0.62/0.70 tff(944,plain,
% 0.62/0.70 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[943, 941])).
% 0.62/0.70 tff(945,plain,
% 0.62/0.70 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(946,plain,
% 0.62/0.70 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.62/0.70 tff(947,plain,
% 0.62/0.70 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[946, 940, 544])).
% 0.62/0.70 tff(948,plain,
% 0.62/0.70 (big_r(sk9, sk2(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[947, 884, 545])).
% 0.62/0.70 tff(949,assumption,(big_r(sk2(sk7), sk1(sk7))), introduced(assumption)).
% 0.62/0.70 tff(950,assumption,(big_r(sk7, sk2(sk7))), introduced(assumption)).
% 0.62/0.70 tff(951,plain,
% 0.62/0.70 ($false),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[295, 265, 950, 949, 948, 927, 906, 905])).
% 0.62/0.70 tff(952,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,[]))).
% 0.62/0.70 tff(953,plain,
% 0.62/0.70 (big_r(sk9, sk6(sk9))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[952, 883, 882, 881, 543, 544])).
% 0.62/0.70 tff(954,plain,
% 0.62/0.70 (^[Y1: $i, W1: $i, X1: $i] : refl((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(955,plain,
% 0.62/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[954])).
% 0.62/0.70 tff(956,plain,
% 0.62/0.70 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(957,plain,
% 0.62/0.70 (^[Y1: $i, W1: $i, X1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), ((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)) | $false | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))))), rewrite((big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | $false | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1))) <=> (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | 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_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(958,plain,
% 0.62/0.71 (![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))) <=> ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[957])).
% 0.62/0.71 tff(959,plain,
% 0.62/0.71 (^[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)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(960,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[959])).
% 0.62/0.71 tff(961,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/sandbox/benchmark/theBenchmark.p','pel38_20')).
% 0.62/0.71 tff(962,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.62/0.71 tff(963,plain,
% 0.62/0.71 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[962, 958])).
% 0.62/0.71 tff(964,plain,
% 0.62/0.71 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[963, 956])).
% 0.62/0.71 tff(965,plain,(
% 0.62/0.71 ![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.71 inference(skolemize,[status(sab)],[964])).
% 0.62/0.71 tff(966,plain,
% 0.62/0.71 (![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[965, 955])).
% 0.62/0.71 tff(967,plain,
% 0.62/0.71 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(968,plain,
% 0.62/0.71 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10))) <=> (big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(969,plain,
% 0.62/0.71 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.62/0.71 inference(monotonicity,[status(thm)],[968])).
% 0.62/0.71 tff(970,plain,
% 0.62/0.71 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.71 inference(transitivity,[status(thm)],[969, 967])).
% 0.62/0.71 tff(971,plain,
% 0.62/0.71 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk7)) | big_p(sk7) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(972,plain,
% 0.62/0.71 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk7) | big_p(sk3(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.62/0.71 tff(973,plain,
% 0.62/0.71 (big_p(sk3(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[972, 966, 545, 4, 544])).
% 0.62/0.71 tff(974,plain,
% 0.62/0.71 (big_p(sk3(sk7))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[973, 100])).
% 0.62/0.71 tff(975,plain,
% 0.62/0.71 (^[L3: $i, N3: $i, M3: $i, K3: $i] : refl(((~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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(976,plain,
% 0.62/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[975])).
% 0.62/0.71 tff(977,plain,
% 0.62/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(978,plain,
% 0.62/0.71 (^[L3: $i, N3: $i, M3: $i, K3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))) <=> ($false | (~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3))))), rewrite(($false | (~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(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))) <=> ((~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(979,plain,
% 0.62/0.71 (![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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[978])).
% 0.62/0.71 tff(980,plain,
% 0.62/0.71 (^[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)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(981,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[980])).
% 0.62/0.71 tff(982,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/sandbox/benchmark/theBenchmark.p','pel38_32')).
% 0.62/0.71 tff(983,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[982, 981])).
% 0.62/0.71 tff(984,plain,
% 0.62/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[983, 979])).
% 0.62/0.71 tff(985,plain,
% 0.62/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[984, 977])).
% 0.62/0.71 tff(986,plain,(
% 0.62/0.71 ![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(skolemize,[status(sab)],[985])).
% 0.62/0.71 tff(987,plain,
% 0.62/0.71 (![L3: $i, N3: $i, M3: $i, K3: $i] : ((~big_p(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[986, 976])).
% 0.62/0.71 tff(988,plain,
% 0.62/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(989,plain,
% 0.62/0.71 (((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(990,plain,
% 0.62/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))))),
% 0.62/0.71 inference(monotonicity,[status(thm)],[989])).
% 0.62/0.71 tff(991,plain,
% 0.62/0.71 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9)))),
% 0.62/0.71 inference(transitivity,[status(thm)],[990, 988])).
% 0.62/0.71 tff(992,plain,
% 0.62/0.71 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(993,plain,
% 0.62/0.71 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.62/0.71 tff(994,plain,
% 0.62/0.71 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[993, 987, 544])).
% 0.62/0.71 tff(995,plain,
% 0.62/0.71 (big_p(sk5(sk9))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[994, 100, 545])).
% 0.62/0.71 tff(996,plain,
% 0.62/0.71 (big_p(sk1(sk7))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[880, 4, 545, 544])).
% 0.62/0.71 tff(997,plain,
% 0.62/0.71 (big_r(sk9, sk6(sk9))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[952, 875, 812, 996, 545, 544])).
% 0.62/0.71 tff(998,plain,
% 0.62/0.71 (^[A4: $i, C4: $i, B4: $i, D4: $i] : refl(((~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(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(999,plain,
% 0.62/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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_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)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[998])).
% 0.62/0.71 tff(1000,plain,
% 0.62/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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_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)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(1001,plain,
% 0.62/0.71 (^[A4: $i, C4: $i, B4: $i, D4: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4))) <=> ($false | (~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(($false | (~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(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(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(1002,plain,
% 0.62/0.71 (![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_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)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[1001])).
% 0.62/0.71 tff(1003,plain,
% 0.62/0.71 (^[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)))))),
% 0.62/0.71 inference(bind,[status(th)],[])).
% 0.62/0.71 tff(1004,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(quant_intro,[status(thm)],[1003])).
% 0.62/0.71 tff(1005,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/sandbox/benchmark/theBenchmark.p','pel38_36')).
% 0.62/0.71 tff(1006,plain,
% 0.62/0.71 (![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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.62/0.71 tff(1007,plain,
% 0.62/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[1006, 1002])).
% 0.62/0.71 tff(1008,plain,
% 0.62/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[1007, 1000])).
% 0.62/0.71 tff(1009,plain,(
% 0.62/0.71 ![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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)))),
% 0.62/0.71 inference(skolemize,[status(sab)],[1008])).
% 0.62/0.71 tff(1010,plain,
% 0.62/0.71 (![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[1009, 999])).
% 0.62/0.71 tff(1011,plain,
% 0.62/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(1012,plain,
% 0.62/0.71 (((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(1013,plain,
% 0.62/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.62/0.71 inference(monotonicity,[status(thm)],[1012])).
% 0.62/0.71 tff(1014,plain,
% 0.62/0.71 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.71 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.62/0.71 tff(1015,plain,
% 0.62/0.71 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(1016,plain,
% 0.62/0.71 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.62/0.72 tff(1017,plain,
% 0.62/0.72 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[1016, 1010, 544])).
% 0.62/0.72 tff(1018,plain,
% 0.62/0.72 (big_r(sk6(sk9), sk5(sk9))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[1017, 100, 545])).
% 0.62/0.72 tff(1019,plain,
% 0.62/0.72 ($false),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[809, 265, 878, 675, 1018, 997, 995, 974])).
% 0.62/0.72 tff(1020,plain,(big_r(sk2(sk9), sk1(sk9)) | (~big_p(sk10)) | big_p(sk7) | (~big_r(sk9, sk10))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.72 tff(1021,plain,
% 0.62/0.72 (big_r(sk2(sk9), sk1(sk9))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[1020, 543, 4, 544])).
% 0.62/0.72 tff(1022,assumption,(~big_r(sk6(sk9), sk5(sk9))), introduced(assumption)).
% 0.62/0.72 tff(1023,plain,
% 0.62/0.72 (^[T3: $i, S3: $i, U3: $i, V3: $i] : refl(((~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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))))),
% 0.62/0.72 inference(bind,[status(th)],[])).
% 0.62/0.72 tff(1024,plain,
% 0.62/0.72 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(quant_intro,[status(thm)],[1023])).
% 0.62/0.72 tff(1025,plain,
% 0.62/0.72 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(1026,plain,
% 0.62/0.72 (^[T3: $i, S3: $i, U3: $i, V3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))) <=> ($false | (~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3))))), rewrite(($false | (~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(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))) <=> ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))))),
% 0.62/0.72 inference(bind,[status(th)],[])).
% 0.62/0.72 tff(1027,plain,
% 0.62/0.72 (![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))) <=> ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(quant_intro,[status(thm)],[1026])).
% 0.62/0.72 tff(1028,plain,
% 0.62/0.72 (^[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)))))),
% 0.62/0.72 inference(bind,[status(th)],[])).
% 0.62/0.72 tff(1029,plain,
% 0.62/0.72 (![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)))),
% 0.62/0.72 inference(quant_intro,[status(thm)],[1028])).
% 0.62/0.72 tff(1030,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/sandbox/benchmark/theBenchmark.p','pel38_34')).
% 0.62/0.72 tff(1031,plain,
% 0.62/0.72 (![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)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.62/0.72 tff(1032,plain,
% 0.62/0.72 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1031, 1027])).
% 0.62/0.72 tff(1033,plain,
% 0.62/0.72 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1032, 1025])).
% 0.62/0.72 tff(1034,plain,(
% 0.62/0.72 ![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(skolemize,[status(sab)],[1033])).
% 0.62/0.72 tff(1035,plain,
% 0.62/0.72 (![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1034, 1024])).
% 0.62/0.72 tff(1036,plain,
% 0.62/0.72 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(1037,plain,
% 0.62/0.72 (((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(1038,plain,
% 0.62/0.72 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))))),
% 0.62/0.72 inference(monotonicity,[status(thm)],[1037])).
% 0.62/0.72 tff(1039,plain,
% 0.62/0.72 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9)))),
% 0.62/0.72 inference(transitivity,[status(thm)],[1038, 1036])).
% 0.62/0.72 tff(1040,plain,
% 0.62/0.72 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.62/0.72 inference(quant_inst,[status(thm)],[])).
% 0.62/0.72 tff(1041,plain,
% 0.62/0.72 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 0.62/0.72 tff(1042,plain,
% 0.62/0.72 ((~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[1041, 1035, 544])).
% 0.62/0.72 tff(1043,plain,
% 0.62/0.72 (big_p(sk1(sk9))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[1042, 1022, 545])).
% 0.62/0.72 tff(1044,plain,
% 0.62/0.72 (^[Z3: $i, Y3: $i, X3: $i, W3: $i] : refl((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(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))))),
% 0.62/0.72 inference(bind,[status(th)],[])).
% 0.62/0.72 tff(1045,plain,
% 0.62/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.62/0.72 inference(quant_intro,[status(thm)],[1044])).
% 0.62/0.72 tff(1046,plain,
% 0.62/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(1047,plain,
% 0.62/0.72 (^[Z3: $i, Y3: $i, X3: $i, W3: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3))) <=> ($false | 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(($false | 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(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(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(1048,plain,
% 0.70/0.72 (![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_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[1047])).
% 0.70/0.72 tff(1049,plain,
% 0.70/0.72 (^[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)))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(1050,plain,
% 0.70/0.72 (![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)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[1049])).
% 0.70/0.72 tff(1051,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/sandbox/benchmark/theBenchmark.p','pel38_35')).
% 0.70/0.72 tff(1052,plain,
% 0.70/0.72 (![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)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 0.70/0.72 tff(1053,plain,
% 0.70/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1052, 1048])).
% 0.70/0.72 tff(1054,plain,
% 0.70/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1053, 1046])).
% 0.70/0.72 tff(1055,plain,(
% 0.70/0.72 ![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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)))),
% 0.70/0.72 inference(skolemize,[status(sab)],[1054])).
% 0.70/0.72 tff(1056,plain,
% 0.70/0.72 (![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1055, 1045])).
% 0.70/0.72 tff(1057,plain,
% 0.70/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(1058,plain,
% 0.70/0.72 ((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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(1059,plain,
% 0.70/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[1058])).
% 0.70/0.72 tff(1060,plain,
% 0.70/0.72 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[1059, 1057])).
% 0.70/0.72 tff(1061,plain,
% 0.70/0.72 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk9, sk2(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(1062,plain,
% 0.70/0.72 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.70/0.72 tff(1063,plain,
% 0.70/0.72 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[1062, 1056, 544])).
% 0.70/0.72 tff(1064,plain,
% 0.70/0.72 (big_r(sk9, sk2(sk9))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[1063, 1022, 545])).
% 0.70/0.72 tff(1065,assumption,(big_r(sk2(sk9), sk1(sk9))), introduced(assumption)).
% 0.70/0.72 tff(1066,plain,
% 0.70/0.72 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[295, 265, 950, 949, 1065, 906])).
% 0.70/0.72 tff(1067,plain,
% 0.70/0.72 ($false),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[1066, 1064, 1043])).
% 0.70/0.72 tff(1068,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,[]))).
% 0.70/0.72 tff(1069,plain,
% 0.70/0.72 (big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[1068, 883, 882, 1021, 881, 543, 544])).
% 0.70/0.72 tff(1070,plain,
% 0.70/0.72 (((~![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))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(1071,plain,
% 0.70/0.72 (((~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))))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(1072,plain,
% 0.70/0.72 (((~![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)))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[1071])).
% 0.70/0.72 tff(1073,plain,
% 0.70/0.72 (((~![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))))),
% 0.70/0.72 inference(transitivity,[status(thm)],[1072, 1070])).
% 0.70/0.72 tff(1074,plain,
% 0.70/0.72 ((~![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))))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(1075,plain,
% 0.70/0.72 ((~![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)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.70/0.72 tff(1076,plain,
% 0.70/0.72 (~big_p(sk5(sk9))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[1075, 265, 883, 882, 881, 1069, 953])).
% 0.70/0.72 tff(1077,plain,
% 0.70/0.72 (^[U2: $i, W2: $i, X2: $i, V2: $i] : refl(((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(1078,plain,
% 0.70/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[1077])).
% 0.70/0.72 tff(1079,plain,
% 0.70/0.72 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(1080,plain,
% 0.70/0.72 (^[U2: $i, W2: $i, X2: $i, V2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ($false | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))))), rewrite(($false | (~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2))) <=> ((~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))) <=> ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(1081,plain,
% 0.70/0.72 (![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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[1080])).
% 0.70/0.72 tff(1082,plain,
% 0.70/0.72 (^[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)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1083,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1082])).
% 0.70/0.73 tff(1084,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/sandbox/benchmark/theBenchmark.p','pel38_28')).
% 0.70/0.73 tff(1085,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.70/0.73 tff(1086,plain,
% 0.70/0.73 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1085, 1081])).
% 0.70/0.73 tff(1087,plain,
% 0.70/0.73 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1086, 1079])).
% 0.70/0.73 tff(1088,plain,(
% 0.70/0.73 ![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[1087])).
% 0.70/0.73 tff(1089,plain,
% 0.70/0.73 (![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1088, 1078])).
% 0.70/0.73 tff(1090,plain,
% 0.70/0.73 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1091,plain,
% 0.70/0.73 (((~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9))) <=> ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1092,plain,
% 0.70/0.73 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[1091])).
% 0.70/0.73 tff(1093,plain,
% 0.70/0.73 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(transitivity,[status(thm)],[1092, 1090])).
% 0.70/0.73 tff(1094,plain,
% 0.70/0.73 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk10)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | big_p(sk1(sk9)))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(1095,plain,
% 0.70/0.73 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 0.70/0.73 tff(1096,plain,
% 0.70/0.73 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1095, 1089, 544])).
% 0.70/0.73 tff(1097,plain,
% 0.70/0.73 (big_p(sk1(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1096, 1076, 543])).
% 0.70/0.73 tff(1098,plain,
% 0.70/0.73 (^[A3: $i, Y2: $i, B3: $i, Z2: $i] : refl((big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1099,plain,
% 0.70/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1098])).
% 0.70/0.73 tff(1100,plain,
% 0.70/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1101,plain,
% 0.70/0.73 (^[A3: $i, Y2: $i, B3: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> ($false | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))))), rewrite(($false | big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3))) <=> (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))) <=> (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1102,plain,
% 0.70/0.73 (![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))) <=> ![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1101])).
% 0.70/0.73 tff(1103,plain,
% 0.70/0.73 (^[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)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1104,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1103])).
% 0.70/0.73 tff(1105,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/sandbox/benchmark/theBenchmark.p','pel38_29')).
% 0.70/0.73 tff(1106,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.70/0.73 tff(1107,plain,
% 0.70/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1106, 1102])).
% 0.70/0.73 tff(1108,plain,
% 0.70/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1107, 1100])).
% 0.70/0.73 tff(1109,plain,(
% 0.70/0.73 ![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[1108])).
% 0.70/0.73 tff(1110,plain,
% 0.70/0.73 (![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1109, 1099])).
% 0.70/0.73 tff(1111,plain,
% 0.70/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))) <=> ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1112,plain,
% 0.70/0.73 ((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(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1113,plain,
% 0.70/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[1112])).
% 0.70/0.73 tff(1114,plain,
% 0.70/0.73 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)))),
% 0.70/0.73 inference(transitivity,[status(thm)],[1113, 1111])).
% 0.70/0.73 tff(1115,plain,
% 0.70/0.73 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk9, sk2(sk9)) | big_p(sk5(sk9)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(1116,plain,
% 0.70/0.73 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.70/0.73 tff(1117,plain,
% 0.70/0.73 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1116, 1110, 544])).
% 0.70/0.73 tff(1118,plain,
% 0.70/0.73 (big_r(sk9, sk2(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1117, 1076, 543])).
% 0.70/0.73 tff(1119,plain,
% 0.70/0.73 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[295, 265, 883, 882, 1021, 881])).
% 0.70/0.73 tff(1120,plain,
% 0.70/0.73 ($false),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1119, 1118, 1097])).
% 0.70/0.73 tff(1121,plain,(big_p(sk7) | (~big_r(sk9, sk10)) | (~big_p(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.73 tff(1122,plain,
% 0.70/0.73 ($false),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1121, 500, 4, 456])).
% 0.70/0.73 tff(1123,plain,(big_p(sk7)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.73 tff(1124,assumption,(~big_p(sk3(sk9))), introduced(assumption)).
% 0.70/0.73 tff(1125,plain,
% 0.70/0.73 (big_p(sk1(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[453, 1124])).
% 0.70/0.73 tff(1126,assumption,(~big_r(sk7, sk8)), introduced(assumption)).
% 0.70/0.73 tff(1127,plain,
% 0.70/0.73 (big_p(sk7)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[455, 5])).
% 0.70/0.73 tff(1128,plain,
% 0.70/0.73 (big_r(sk2(sk9), sk1(sk9)) | big_p(sk3(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[126, 113, 5])).
% 0.70/0.73 tff(1129,plain,
% 0.70/0.73 (big_p(sk3(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1128, 100])).
% 0.70/0.73 tff(1130,assumption,(big_p(sk7)), introduced(assumption)).
% 0.70/0.73 tff(1131,plain,
% 0.70/0.73 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[168, 386])).
% 0.70/0.73 tff(1132,plain,
% 0.70/0.73 (^[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))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1133,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1132])).
% 0.70/0.73 tff(1134,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1135,plain,
% 0.70/0.73 (^[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)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(1136,plain,
% 0.70/0.73 (![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)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[1135])).
% 0.70/0.73 tff(1137,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/sandbox/benchmark/theBenchmark.p','pel38_43')).
% 0.70/0.73 tff(1138,plain,
% 0.70/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.70/0.73 tff(1139,plain,
% 0.70/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1138, 1134])).
% 0.70/0.73 tff(1140,plain,(
% 0.70/0.73 ![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[1139])).
% 0.70/0.73 tff(1141,plain,
% 0.70/0.73 (![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1140, 1133])).
% 0.70/0.73 tff(1142,plain,
% 0.70/0.73 (((~![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))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1143,plain,
% 0.70/0.73 (((~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))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1144,plain,
% 0.70/0.73 (((~![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)))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[1143])).
% 0.70/0.73 tff(1145,plain,
% 0.70/0.73 (((~![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))))),
% 0.70/0.73 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.70/0.73 tff(1146,plain,
% 0.70/0.73 ((~![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))))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(1147,plain,
% 0.70/0.73 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.70/0.73 tff(1148,plain,
% 0.70/0.73 (~big_p(sk3(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1147, 1130, 1126, 1141, 334, 56])).
% 0.70/0.73 tff(1149,plain,
% 0.70/0.73 ($false),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[340, 232, 5, 3, 1148])).
% 0.70/0.73 tff(1150,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9) | (~big_p(sk7)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.73 tff(1151,plain,
% 0.70/0.73 (big_r(sk9, sk2(sk9))),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[1150, 5, 1130, 1126])).
% 0.70/0.73 tff(1152,plain,
% 0.70/0.73 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(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(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(1153,plain,
% 0.70/0.73 (((~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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1154,plain,
% 0.70/0.74 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[1153])).
% 0.70/0.74 tff(1155,plain,
% 0.70/0.74 (((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.74 inference(transitivity,[status(thm)],[1154, 1152])).
% 0.70/0.74 tff(1156,plain,
% 0.70/0.74 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | ((~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(1157,plain,
% 0.70/0.74 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.70/0.74 tff(1158,plain,
% 0.70/0.74 (~big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1157, 1130, 1126, 1141, 1151, 1131])).
% 0.70/0.74 tff(1159,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[392, 70, 5, 386, 1158])).
% 0.70/0.74 tff(1160,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | (~big_p(sk7)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1161,plain,
% 0.70/0.74 (big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1160, 5, 1130, 1126])).
% 0.70/0.74 tff(1162,plain,
% 0.70/0.74 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1147, 1130, 1126, 1141, 1161])).
% 0.70/0.74 tff(1163,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1162, 1129, 148])).
% 0.70/0.74 tff(1164,plain,(big_r(sk2(sk9), sk1(sk9)) | (~big_p(sk7)) | big_r(sk7, sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1165,plain,
% 0.70/0.74 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1164, 5, 1126, 1127])).
% 0.70/0.74 tff(1166,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1150, 1127, 5, 1126])).
% 0.70/0.74 tff(1167,plain,
% 0.70/0.74 (~big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1157, 1127, 1126, 1141, 1166, 1165])).
% 0.70/0.74 tff(1168,plain,
% 0.70/0.74 (big_r(sk9, sk4(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[366, 183, 5, 1167])).
% 0.70/0.74 tff(1169,plain,
% 0.70/0.74 (big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1160, 1127, 5, 1126])).
% 0.70/0.74 tff(1170,plain,
% 0.70/0.74 (~big_p(sk3(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1147, 1127, 1126, 1141, 1169, 1168])).
% 0.70/0.74 tff(1171,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[452, 19, 5, 1167, 1170])).
% 0.70/0.74 tff(1172,plain,(big_p(sk9) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1173,plain,
% 0.70/0.74 (big_p(sk9)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1172, 1126])).
% 0.70/0.74 tff(1174,plain,
% 0.70/0.74 (big_p(sk7)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[499, 457])).
% 0.70/0.74 tff(1175,plain,
% 0.70/0.74 (((~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))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1176,plain,
% 0.70/0.74 (((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))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1177,plain,
% 0.70/0.74 (((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) <=> (big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1178,plain,
% 0.70/0.74 ((((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)))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[1177])).
% 0.70/0.74 tff(1179,plain,
% 0.70/0.74 ((((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))),
% 0.70/0.74 inference(transitivity,[status(thm)],[1178, 1176])).
% 0.70/0.74 tff(1180,axiom,(((big_r(sk7, sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel38_41')).
% 0.70/0.74 tff(1181,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.70/0.74 tff(1182,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1181, 1175])).
% 0.70/0.74 tff(1183,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1182, 1175])).
% 0.70/0.74 tff(1184,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1183, 1175])).
% 0.70/0.74 tff(1185,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1184, 1175])).
% 0.70/0.74 tff(1186,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1185, 1175])).
% 0.70/0.74 tff(1187,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1186, 1175])).
% 0.70/0.74 tff(1188,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1187, 1175])).
% 0.70/0.74 tff(1189,plain,
% 0.70/0.74 ((~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1188, 1175])).
% 0.70/0.74 tff(1190,plain,
% 0.70/0.74 (~big_p(sk9)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1189, 1174, 457, 1126])).
% 0.70/0.74 tff(1191,plain,
% 0.70/0.74 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1164, 1174, 1126, 1190])).
% 0.70/0.74 tff(1192,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1150, 1190, 1174, 1126])).
% 0.70/0.74 tff(1193,plain,
% 0.70/0.74 (~big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1157, 1174, 1126, 1141, 1192, 1191])).
% 0.70/0.74 tff(1194,plain,
% 0.70/0.74 (big_p(sk3(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[452, 19, 1190, 1193])).
% 0.70/0.74 tff(1195,plain,
% 0.70/0.74 (big_r(sk9, sk4(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[366, 183, 1190, 1193])).
% 0.70/0.74 tff(1196,plain,
% 0.70/0.74 (big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1160, 1190, 1174, 1126])).
% 0.70/0.74 tff(1197,plain,
% 0.70/0.74 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1147, 1174, 1126, 1141, 1196])).
% 0.70/0.74 tff(1198,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1197, 1195, 1194])).
% 0.70/0.74 tff(1199,plain,(big_r(sk9, sk10) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1200,plain,
% 0.70/0.74 (big_r(sk9, sk10)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1199, 1126])).
% 0.70/0.74 tff(1201,plain,
% 0.70/0.74 (big_p(sk7)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1121, 1200, 1173])).
% 0.70/0.74 tff(1202,plain,
% 0.70/0.74 ((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)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1203,plain,
% 0.70/0.74 (((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)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1204,plain,
% 0.70/0.74 (((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) <=> (big_p(sk10) | big_r(sk7, sk8) | (~big_p(sk7)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1205,plain,
% 0.70/0.74 ((((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)))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[1204])).
% 0.70/0.74 tff(1206,plain,
% 0.70/0.74 ((((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)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.70/0.74 tff(1207,axiom,(((big_p(sk10) | big_r(sk7, sk8)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel38_40')).
% 0.70/0.74 tff(1208,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.70/0.74 tff(1209,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1208, 1202])).
% 0.70/0.74 tff(1210,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1209, 1202])).
% 0.70/0.74 tff(1211,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1210, 1202])).
% 0.70/0.74 tff(1212,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1211, 1202])).
% 0.70/0.74 tff(1213,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1212, 1202])).
% 0.70/0.74 tff(1214,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1213, 1202])).
% 0.70/0.74 tff(1215,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1214, 1202])).
% 0.70/0.74 tff(1216,plain,
% 0.70/0.74 (big_p(sk10) | (~big_p(sk9)) | big_r(sk7, sk8) | (~big_p(sk7))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1215, 1202])).
% 0.70/0.74 tff(1217,plain,
% 0.70/0.74 (big_p(sk10)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1216, 1201, 1173, 1126])).
% 0.70/0.74 tff(1218,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[903, 897, 1200])).
% 0.70/0.74 tff(1219,plain,
% 0.70/0.74 (big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1218, 884, 1217])).
% 0.70/0.74 tff(1220,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[946, 940, 1200])).
% 0.70/0.74 tff(1221,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1220, 884, 1217])).
% 0.70/0.74 tff(1222,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[993, 987, 1200])).
% 0.70/0.74 tff(1223,plain,
% 0.70/0.74 (big_p(sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1222, 100, 1217])).
% 0.70/0.74 tff(1224,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[925, 919, 1200])).
% 0.70/0.74 tff(1225,plain,
% 0.70/0.74 (big_r(sk9, sk6(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1224, 100, 1217])).
% 0.70/0.74 tff(1226,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1016, 1010, 1200])).
% 0.70/0.74 tff(1227,plain,
% 0.70/0.74 (big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1226, 100, 1217])).
% 0.70/0.74 tff(1228,plain,
% 0.70/0.74 (((~![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))))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1229,plain,
% 0.70/0.74 (((~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))))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1230,plain,
% 0.70/0.74 (((~![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)))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[1229])).
% 0.70/0.74 tff(1231,plain,
% 0.70/0.74 (((~![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))))),
% 0.70/0.74 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.70/0.74 tff(1232,plain,
% 0.70/0.74 ((~![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))))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(1233,plain,
% 0.70/0.74 ((~![G4: $i, H4: $i] : ((~big_p(G4)) | (~big_r(H4, G4)) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk9, H4)))) | big_r(sk7, sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.70/0.74 tff(1234,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1233, 1201, 1126, 1141, 1227, 1225, 1223])).
% 0.70/0.74 tff(1235,plain,(big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1236,plain,
% 0.70/0.74 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1235, 1126])).
% 0.70/0.74 tff(1237,plain,
% 0.70/0.74 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1157, 1201, 1126, 1141, 1236])).
% 0.70/0.74 tff(1238,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1237, 1221, 1219])).
% 0.70/0.74 tff(1239,plain,(big_r(sk9, sk6(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1240,plain,
% 0.70/0.74 (big_r(sk9, sk6(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1239, 1126])).
% 0.70/0.74 tff(1241,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1041, 1035, 1200])).
% 0.70/0.74 tff(1242,plain,
% 0.70/0.74 (big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1241, 1022, 1217])).
% 0.70/0.74 tff(1243,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1062, 1056, 1200])).
% 0.70/0.74 tff(1244,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1243, 1022, 1217])).
% 0.70/0.74 tff(1245,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1237, 1244, 1242])).
% 0.70/0.74 tff(1246,plain,(big_r(sk6(sk9), sk5(sk9)) | big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1247,plain,
% 0.70/0.74 (big_r(sk6(sk9), sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1246, 1126])).
% 0.70/0.74 tff(1248,plain,
% 0.70/0.74 ((~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1233, 1201, 1126, 1141, 1247])).
% 0.70/0.74 tff(1249,plain,
% 0.70/0.74 (~big_p(sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1248, 1240])).
% 0.70/0.74 tff(1250,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1095, 1089, 1200])).
% 0.70/0.74 tff(1251,plain,
% 0.70/0.74 (big_p(sk1(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1250, 1249, 1217])).
% 0.70/0.74 tff(1252,plain,
% 0.70/0.74 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1116, 1110, 1200])).
% 0.70/0.74 tff(1253,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1252, 1249, 1217])).
% 0.70/0.74 tff(1254,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[1237, 1253, 1251])).
% 0.70/0.74 tff(1255,plain,(big_r(sk7, sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(1256,plain,
% 0.70/0.74 (big_r(sk9, sk2(sk9))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[333, 386])).
% 0.70/0.74 tff(1257,plain,
% 0.70/0.74 (^[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))))),
% 0.70/0.74 inference(bind,[status(th)],[])).
% 0.70/0.74 tff(1258,plain,
% 0.70/0.74 (![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)))),
% 0.70/0.74 inference(quant_intro,[status(thm)],[1257])).
% 0.70/0.74 tff(1259,plain,
% 0.70/0.74 (![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)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1260,plain,
% 0.70/0.74 (^[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)))))),
% 0.70/0.74 inference(bind,[status(th)],[])).
% 0.70/0.74 tff(1261,plain,
% 0.70/0.74 (![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)))),
% 0.70/0.74 inference(quant_intro,[status(thm)],[1260])).
% 0.70/0.74 tff(1262,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/sandbox/benchmark/theBenchmark.p','pel38_42')).
% 0.70/0.74 tff(1263,plain,
% 0.70/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.70/0.74 tff(1264,plain,
% 0.70/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1263, 1259])).
% 0.70/0.74 tff(1265,plain,(
% 0.70/0.74 ![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.70/0.74 inference(skolemize,[status(sab)],[1264])).
% 0.70/0.74 tff(1266,plain,
% 0.70/0.74 (![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[1265, 1258])).
% 0.70/0.74 tff(1267,plain,
% 0.70/0.74 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(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(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(1268,plain,
% 0.70/0.74 ((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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1269,plain,
% 0.70/0.75 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1268])).
% 0.70/0.75 tff(1270,plain,
% 0.70/0.75 (((~![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_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1269, 1267])).
% 0.70/0.75 tff(1271,plain,
% 0.70/0.75 ((~![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))))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1272,plain,
% 0.70/0.75 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9))) | (~big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.70/0.75 tff(1273,plain,
% 0.70/0.75 (~big_p(sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1272, 2, 1123, 1266, 1256, 1131])).
% 0.70/0.75 tff(1274,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[392, 70, 5, 386, 1273])).
% 0.70/0.75 tff(1275,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(1276,plain,
% 0.70/0.75 (big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1275, 2, 5])).
% 0.70/0.75 tff(1277,plain,
% 0.70/0.75 (((~![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))))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1278,plain,
% 0.70/0.75 ((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))))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1279,plain,
% 0.70/0.75 (((~![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)))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1278])).
% 0.70/0.75 tff(1280,plain,
% 0.70/0.75 (((~![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))))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.70/0.75 tff(1281,plain,
% 0.70/0.75 ((~![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))))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1282,plain,
% 0.70/0.75 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.70/0.75 tff(1283,plain,
% 0.70/0.75 ((~big_p(sk3(sk9))) | (~big_r(sk9, sk4(sk9)))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1282, 2, 1123, 1266, 1276])).
% 0.70/0.75 tff(1284,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1283, 342, 56])).
% 0.70/0.75 tff(1285,plain,(big_r(sk9, sk2(sk9)) | big_p(sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(1286,plain,
% 0.70/0.75 (big_r(sk9, sk2(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1285, 2, 5])).
% 0.70/0.75 tff(1287,plain,
% 0.70/0.75 (~big_p(sk3(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1283, 148])).
% 0.70/0.75 tff(1288,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[126, 113, 5, 100, 1287])).
% 0.70/0.75 tff(1289,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(1290,plain,
% 0.70/0.75 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1289, 2, 5])).
% 0.70/0.75 tff(1291,plain,
% 0.70/0.75 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1272, 2, 1123, 1266, 1290])).
% 0.70/0.75 tff(1292,plain,
% 0.70/0.75 (~big_p(sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1291, 1286])).
% 0.70/0.75 tff(1293,plain,
% 0.70/0.75 (big_p(sk3(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[453, 1292])).
% 0.70/0.75 tff(1294,plain,
% 0.70/0.75 (big_r(sk9, sk4(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[367, 1292])).
% 0.70/0.75 tff(1295,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1283, 1294, 1293])).
% 0.70/0.75 tff(1296,plain,(big_p(sk8) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(1297,plain,
% 0.70/0.75 (big_p(sk8)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1296, 5])).
% 0.70/0.75 tff(1298,plain,
% 0.70/0.75 (^[M1: $i, L1: $i, K1: $i] : refl((big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))))),
% 0.70/0.75 inference(bind,[status(th)],[])).
% 0.70/0.75 tff(1299,plain,
% 0.70/0.75 (![M1: $i, L1: $i, K1: $i] : (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(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(quant_intro,[status(thm)],[1298])).
% 0.70/0.75 tff(1300,plain,
% 0.70/0.75 (![M1: $i, L1: $i, K1: $i] : (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(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1301,plain,
% 0.70/0.75 (^[M1: $i, L1: $i, K1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> ($false | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))))), rewrite(($false | big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1))) <=> (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))) <=> (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))))),
% 0.70/0.75 inference(bind,[status(th)],[])).
% 0.70/0.75 tff(1302,plain,
% 0.70/0.75 (![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))) <=> ![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(quant_intro,[status(thm)],[1301])).
% 0.70/0.75 tff(1303,plain,
% 0.70/0.75 (^[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)))))),
% 0.70/0.75 inference(bind,[status(th)],[])).
% 0.70/0.75 tff(1304,plain,
% 0.70/0.75 (![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)))),
% 0.70/0.75 inference(quant_intro,[status(thm)],[1303])).
% 0.70/0.75 tff(1305,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/sandbox/benchmark/theBenchmark.p','pel38_16')).
% 0.70/0.75 tff(1306,plain,
% 0.70/0.75 (![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)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.70/0.75 tff(1307,plain,
% 0.70/0.75 (![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1306, 1302])).
% 0.70/0.75 tff(1308,plain,
% 0.70/0.75 (![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1307, 1300])).
% 0.70/0.75 tff(1309,plain,(
% 0.70/0.75 ![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(skolemize,[status(sab)],[1308])).
% 0.70/0.75 tff(1310,plain,
% 0.70/0.75 (![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1309, 1299])).
% 0.70/0.75 tff(1311,plain,
% 0.70/0.75 (((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))) <=> ((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1312,plain,
% 0.70/0.75 ((big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1313,plain,
% 0.70/0.75 (((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (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(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1312])).
% 0.70/0.75 tff(1314,plain,
% 0.70/0.75 (((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (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(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1313, 1311])).
% 0.70/0.75 tff(1315,plain,
% 0.70/0.75 ((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | (big_p(sk3(sk9)) | big_p(sk1(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1316,plain,
% 0.70/0.75 ((~![M1: $i, L1: $i, K1: $i] : (big_p(sk3(K1)) | big_p(sk1(L1)) | big_p(K1) | (~big_r(L1, M1)) | (~big_p(M1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.70/0.75 tff(1317,plain,
% 0.70/0.75 (big_p(sk1(sk7)) | big_p(sk3(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1316, 1310, 1297, 5, 1255])).
% 0.70/0.75 tff(1318,plain,
% 0.70/0.75 (big_p(sk1(sk7))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1317, 1124])).
% 0.70/0.75 tff(1319,plain,
% 0.70/0.75 (((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1320,plain,
% 0.70/0.75 ((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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1321,plain,
% 0.70/0.75 (((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1320])).
% 0.70/0.75 tff(1322,plain,
% 0.70/0.75 (((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1321, 1319])).
% 0.70/0.75 tff(1323,plain,
% 0.70/0.75 ((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1324,plain,
% 0.70/0.75 ((~![M2: $i, L2: $i, N2: $i] : (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(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 0.70/0.75 tff(1325,plain,
% 0.70/0.75 ((~big_p(sk8)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1324, 753, 5, 1255])).
% 0.70/0.75 tff(1326,plain,
% 0.70/0.75 (big_p(sk5(sk7))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1325, 100, 1297])).
% 0.70/0.75 tff(1327,plain,
% 0.70/0.75 (((~![O2: $i, P2: $i, Q2: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))) <=> ((~![O2: $i, P2: $i, Q2: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1328,plain,
% 0.70/0.75 ((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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1329,plain,
% 0.70/0.75 (((~![O2: $i, P2: $i, Q2: $i] : (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_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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | (big_p(sk9) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1328])).
% 0.70/0.75 tff(1330,plain,
% 0.70/0.75 (((~![O2: $i, P2: $i, Q2: $i] : (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_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(O2) | big_r(P2, sk6(P2)) | (~big_r(P2, Q2)) | (~big_p(Q2)) | big_r(sk2(O2), sk1(O2)))) | big_p(sk9) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.70/0.75 tff(1331,plain,
% 0.70/0.75 ((~![O2: $i, P2: $i, Q2: $i] : (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_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1332,plain,
% 0.70/0.75 ((~![O2: $i, P2: $i, Q2: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.70/0.75 tff(1333,plain,
% 0.70/0.75 ((~big_p(sk8)) | big_r(sk7, sk6(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1332, 774, 5, 1255])).
% 0.70/0.75 tff(1334,plain,
% 0.70/0.75 (big_r(sk7, sk6(sk7))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1333, 100, 1297])).
% 0.70/0.75 tff(1335,plain,
% 0.70/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_p(sk9) | (~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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1336,plain,
% 0.70/0.75 ((big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))) <=> (big_p(sk9) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1337,plain,
% 0.70/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_p(sk9) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1336])).
% 0.70/0.75 tff(1338,plain,
% 0.70/0.75 (((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | 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(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1337, 1335])).
% 0.70/0.75 tff(1339,plain,
% 0.70/0.75 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | (big_r(sk2(sk9), sk1(sk9)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1340,plain,
% 0.70/0.75 ((~![T2: $i, S2: $i, R2: $i] : (big_r(sk2(R2), sk1(R2)) | big_p(R2) | (~big_r(S2, T2)) | (~big_p(T2)) | big_r(sk6(S2), sk5(S2)))) | big_p(sk9) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.70/0.75 tff(1341,plain,
% 0.70/0.75 (big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1340, 795, 1297, 5, 1255])).
% 0.70/0.75 tff(1342,plain,
% 0.70/0.75 (big_r(sk6(sk7), sk5(sk7))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1341, 100])).
% 0.70/0.75 tff(1343,plain,
% 0.70/0.75 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))) <=> ((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1344,plain,
% 0.70/0.75 ((big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(1345,plain,
% 0.70/0.75 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[1344])).
% 0.70/0.75 tff(1346,plain,
% 0.70/0.75 (((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (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(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[1345, 1343])).
% 0.70/0.75 tff(1347,plain,
% 0.70/0.75 ((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | (big_p(sk9) | big_r(sk9, sk4(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(1348,plain,
% 0.70/0.75 ((~![R1: $i, S1: $i, Q1: $i] : (big_p(Q1) | big_r(Q1, sk4(Q1)) | big_p(sk1(R1)) | (~big_r(R1, S1)) | (~big_p(S1)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.70/0.75 tff(1349,plain,
% 0.70/0.75 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk9, sk4(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1348, 688, 5, 1255])).
% 0.70/0.75 tff(1350,plain,
% 0.70/0.75 (big_p(sk1(sk7))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[1349, 360, 1297])).
% 0.70/0.75 tff(1351,plain,
% 0.70/0.75 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[147, 360])).
% 0.70/0.76 tff(1352,plain,
% 0.70/0.76 (((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1353,plain,
% 0.70/0.76 ((big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7))) <=> (big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1354,plain,
% 0.70/0.76 (((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1353])).
% 0.70/0.76 tff(1355,plain,
% 0.70/0.76 (((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (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(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1354, 1352])).
% 0.70/0.76 tff(1356,plain,
% 0.70/0.76 ((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | (big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1357,plain,
% 0.70/0.76 ((~![W: $i, V: $i, X: $i] : (big_p(V) | big_r(V, sk2(V)) | (~big_p(X)) | (~big_r(W, X)) | big_p(sk5(W)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.70/0.76 tff(1358,plain,
% 0.70/0.76 ((~big_p(sk8)) | big_p(sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1357, 825, 5, 1255])).
% 0.70/0.76 tff(1359,plain,
% 0.70/0.76 (big_p(sk5(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1358, 3, 1297])).
% 0.70/0.76 tff(1360,plain,
% 0.70/0.76 (((~![Z: $i, A1: $i, Y: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![Z: $i, A1: $i, Y: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1361,plain,
% 0.70/0.76 ((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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1362,plain,
% 0.70/0.76 (((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk9) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1361])).
% 0.70/0.76 tff(1363,plain,
% 0.70/0.76 (((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (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(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | big_p(sk9) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1362, 1360])).
% 0.70/0.76 tff(1364,plain,
% 0.70/0.76 ((~![Z: $i, A1: $i, Y: $i] : (big_p(Y) | big_r(Y, sk2(Y)) | (~big_r(Z, A1)) | (~big_p(A1)) | big_r(Z, sk6(Z)))) | (big_p(sk9) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1365,plain,
% 0.70/0.76 ((~![Z: $i, A1: $i, Y: $i] : (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(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.70/0.76 tff(1366,plain,
% 0.70/0.76 ((~big_p(sk8)) | big_r(sk7, sk6(sk7)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1365, 843, 5, 1255])).
% 0.70/0.76 tff(1367,plain,
% 0.70/0.76 (big_r(sk7, sk6(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1366, 3, 1297])).
% 0.70/0.76 tff(1368,plain,
% 0.70/0.76 (((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1369,plain,
% 0.70/0.76 ((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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1370,plain,
% 0.70/0.76 (((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1369])).
% 0.70/0.76 tff(1371,plain,
% 0.70/0.76 (((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))) <=> ((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1370, 1368])).
% 0.70/0.76 tff(1372,plain,
% 0.70/0.76 ((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1373,plain,
% 0.70/0.76 ((~![B1: $i, D1: $i, C1: $i] : (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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.70/0.76 tff(1374,plain,
% 0.70/0.76 ((~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1373, 864, 5, 1255])).
% 0.70/0.76 tff(1375,plain,
% 0.70/0.76 (big_r(sk6(sk7), sk5(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1374, 3, 1297])).
% 0.70/0.76 tff(1376,plain,
% 0.70/0.76 (((~![D2: $i, E2: $i, C2: $i] : (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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))) <=> ((~![D2: $i, E2: $i, C2: $i] : (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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1377,plain,
% 0.70/0.76 ((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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1378,plain,
% 0.70/0.76 (((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1377])).
% 0.70/0.76 tff(1379,plain,
% 0.70/0.76 (((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (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(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | big_p(sk9) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1378, 1376])).
% 0.70/0.76 tff(1380,plain,
% 0.70/0.76 ((~![D2: $i, E2: $i, C2: $i] : (big_p(C2) | big_r(sk4(C2), sk3(C2)) | big_p(sk1(D2)) | (~big_r(D2, E2)) | (~big_p(E2)))) | (big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1381,plain,
% 0.70/0.76 ((~![D2: $i, E2: $i, C2: $i] : (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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 0.70/0.76 tff(1382,plain,
% 0.70/0.76 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1381, 621, 5, 1255])).
% 0.70/0.76 tff(1383,plain,
% 0.70/0.76 (big_p(sk1(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1382, 386, 1297])).
% 0.70/0.76 tff(1384,plain,
% 0.70/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_p(sk9) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1385,plain,
% 0.70/0.76 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1386,plain,
% 0.70/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1385])).
% 0.70/0.76 tff(1387,plain,
% 0.70/0.76 (((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | 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(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1386, 1384])).
% 0.70/0.76 tff(1388,plain,
% 0.70/0.76 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk9) | big_r(sk4(sk9), sk3(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1389,plain,
% 0.70/0.76 ((~![K2: $i, I2: $i, J2: $i] : (big_r(sk2(J2), sk1(J2)) | big_p(I2) | big_r(sk4(I2), sk3(I2)) | (~big_p(K2)) | (~big_r(J2, K2)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 0.70/0.76 tff(1390,plain,
% 0.70/0.76 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1389, 642, 5, 1255])).
% 0.70/0.76 tff(1391,plain,
% 0.70/0.76 (big_r(sk2(sk7), sk1(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1390, 386, 1297])).
% 0.70/0.76 tff(1392,plain,
% 0.70/0.76 (((~![G2: $i, H2: $i, F2: $i] : (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_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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1393,plain,
% 0.70/0.76 ((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_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1394,plain,
% 0.70/0.76 (((~![G2: $i, H2: $i, F2: $i] : (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_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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1393])).
% 0.70/0.76 tff(1395,plain,
% 0.70/0.76 (((~![G2: $i, H2: $i, F2: $i] : (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_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(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.70/0.76 tff(1396,plain,
% 0.70/0.76 ((~![G2: $i, H2: $i, F2: $i] : (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_r(sk4(sk9), sk3(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1397,plain,
% 0.70/0.76 ((~![G2: $i, H2: $i, F2: $i] : (big_p(F2) | big_r(sk4(F2), sk3(F2)) | (~big_r(G2, H2)) | (~big_p(H2)) | big_r(G2, sk2(G2)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.70/0.76 tff(1398,plain,
% 0.70/0.76 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1397, 663, 5, 1255])).
% 0.70/0.76 tff(1399,plain,
% 0.70/0.76 (big_r(sk7, sk2(sk7))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1398, 386, 1297])).
% 0.70/0.76 tff(1400,plain,
% 0.70/0.76 (~big_p(sk1(sk9))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[295, 265, 1399, 1391, 1256, 1131, 1383])).
% 0.70/0.76 tff(1401,plain,
% 0.70/0.76 ($false),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[392, 70, 5, 386, 1400])).
% 0.70/0.76 tff(1402,plain,(big_r(sk4(sk9), sk3(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.76 tff(1403,plain,
% 0.70/0.76 (big_r(sk4(sk9), sk3(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1402, 5])).
% 0.70/0.77 tff(1404,plain,
% 0.70/0.77 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1405,plain,
% 0.70/0.77 (((~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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1406,plain,
% 0.70/0.77 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1405])).
% 0.70/0.77 tff(1407,plain,
% 0.70/0.77 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1406, 1404])).
% 0.70/0.77 tff(1408,plain,
% 0.70/0.77 ((~![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))))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1409,plain,
% 0.70/0.77 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_p(sk3(sk9))) | (~big_r(sk4(sk9), sk3(sk9))) | (~big_r(sk9, sk4(sk9))) | (~big_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.70/0.77 tff(1410,plain,
% 0.70/0.77 ($false),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1409, 265, 1403, 56, 1375, 1367, 1359, 342])).
% 0.70/0.77 tff(1411,plain,(big_r(sk9, sk2(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.77 tff(1412,plain,
% 0.70/0.77 (big_r(sk9, sk2(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1411, 5])).
% 0.70/0.77 tff(1413,plain,
% 0.70/0.77 (((~![A2: $i, B2: $i, Z1: $i] : (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_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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1414,plain,
% 0.70/0.77 ((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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1415,plain,
% 0.70/0.77 (((~![A2: $i, B2: $i, Z1: $i] : (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_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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | (big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1414])).
% 0.70/0.77 tff(1416,plain,
% 0.70/0.77 (((~![A2: $i, B2: $i, Z1: $i] : (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_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(Z1) | big_r(Z1, sk4(Z1)) | (~big_r(A2, B2)) | (~big_p(B2)) | big_r(sk2(A2), sk1(A2)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1415, 1413])).
% 0.70/0.77 tff(1417,plain,
% 0.70/0.77 ((~![A2: $i, B2: $i, Z1: $i] : (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_r(sk9, sk4(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1418,plain,
% 0.70/0.77 ((~![A2: $i, B2: $i, Z1: $i] : (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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 0.70/0.77 tff(1419,plain,
% 0.70/0.77 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk9, sk4(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1418, 711, 5, 1255])).
% 0.70/0.77 tff(1420,plain,
% 0.70/0.77 (big_r(sk2(sk7), sk1(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1419, 360, 1297])).
% 0.70/0.77 tff(1421,plain,
% 0.70/0.77 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk9) | 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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1422,plain,
% 0.70/0.77 ((big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1423,plain,
% 0.70/0.77 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1422])).
% 0.70/0.77 tff(1424,plain,
% 0.70/0.77 (((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (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(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9)))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1423, 1421])).
% 0.70/0.77 tff(1425,plain,
% 0.70/0.77 ((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | (big_p(sk9) | big_r(sk7, sk2(sk7)) | big_r(sk9, sk4(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1426,plain,
% 0.70/0.77 ((~![V1: $i, T1: $i, U1: $i] : (big_p(T1) | big_r(U1, sk2(U1)) | big_r(T1, sk4(T1)) | (~big_p(V1)) | (~big_r(U1, V1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk9, sk4(sk9))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 0.70/0.77 tff(1427,plain,
% 0.70/0.77 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk9, sk4(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1426, 732, 5, 1255])).
% 0.70/0.77 tff(1428,plain,
% 0.70/0.77 (big_r(sk7, sk2(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1427, 360, 1297])).
% 0.70/0.77 tff(1429,plain,
% 0.70/0.77 (~big_p(sk1(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[295, 265, 1428, 1420, 1412, 1351, 1350])).
% 0.70/0.77 tff(1430,plain,
% 0.70/0.77 ($false),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[366, 183, 5, 360, 1429])).
% 0.70/0.77 tff(1431,plain,(big_r(sk9, sk4(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.77 tff(1432,plain,
% 0.70/0.77 (big_r(sk9, sk4(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1431, 5])).
% 0.70/0.77 tff(1433,plain,
% 0.70/0.77 ($false),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1409, 265, 1403, 1432, 1342, 1334, 1326, 1129])).
% 0.70/0.77 tff(1434,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.77 tff(1435,plain,
% 0.70/0.77 (big_r(sk2(sk9), sk1(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1434, 5])).
% 0.70/0.77 tff(1436,plain,
% 0.70/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_p(sk9) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1437,plain,
% 0.70/0.77 ((big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8))) <=> (big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1438,plain,
% 0.70/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1437])).
% 0.70/0.77 tff(1439,plain,
% 0.70/0.77 (((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | 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(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.70/0.77 tff(1440,plain,
% 0.70/0.77 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9)) | big_p(sk9) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1441,plain,
% 0.70/0.77 ((~![Y1: $i, W1: $i, X1: $i] : (big_r(sk2(X1), sk1(X1)) | big_p(sk3(W1)) | big_p(W1) | (~big_p(Y1)) | (~big_r(X1, Y1)))) | big_p(sk9) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.70/0.77 tff(1442,plain,
% 0.70/0.77 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk3(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1441, 966, 1297, 5, 1255])).
% 0.70/0.77 tff(1443,plain,
% 0.70/0.77 (big_r(sk2(sk7), sk1(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1442, 1124])).
% 0.70/0.77 tff(1444,plain,
% 0.70/0.77 (^[N1: $i, O1: $i, P1: $i] : refl((big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))))),
% 0.70/0.77 inference(bind,[status(th)],[])).
% 0.70/0.77 tff(1445,plain,
% 0.70/0.77 (![N1: $i, O1: $i, P1: $i] : (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_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(quant_intro,[status(thm)],[1444])).
% 0.70/0.77 tff(1446,plain,
% 0.70/0.77 (![N1: $i, O1: $i, P1: $i] : (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_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1447,plain,
% 0.70/0.77 (^[N1: $i, O1: $i, P1: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(big_p(a)), (big_p(a) <=> $true)), ((~big_p(a)) <=> (~$true))), rewrite((~$true) <=> $false), ((~big_p(a)) <=> $false)), (((~big_p(a)) | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> ($false | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))))), rewrite(($false | big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1))) <=> (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))) <=> (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))))),
% 0.70/0.77 inference(bind,[status(th)],[])).
% 0.70/0.77 tff(1448,plain,
% 0.70/0.77 (![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_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(quant_intro,[status(thm)],[1447])).
% 0.70/0.77 tff(1449,plain,
% 0.70/0.77 (^[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)))))),
% 0.70/0.77 inference(bind,[status(th)],[])).
% 0.70/0.77 tff(1450,plain,
% 0.70/0.77 (![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)))),
% 0.70/0.77 inference(quant_intro,[status(thm)],[1449])).
% 0.70/0.77 tff(1451,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/sandbox/benchmark/theBenchmark.p','pel38_17')).
% 0.70/0.77 tff(1452,plain,
% 0.70/0.77 (![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)))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 0.70/0.77 tff(1453,plain,
% 0.70/0.77 (![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1452, 1448])).
% 0.70/0.77 tff(1454,plain,
% 0.70/0.77 (![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1453, 1446])).
% 0.70/0.77 tff(1455,plain,(
% 0.70/0.77 ![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(skolemize,[status(sab)],[1454])).
% 0.70/0.77 tff(1456,plain,
% 0.70/0.77 (![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1455, 1445])).
% 0.70/0.77 tff(1457,plain,
% 0.70/0.77 (((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))) <=> ((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1458,plain,
% 0.70/0.77 ((big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9))) <=> (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1459,plain,
% 0.70/0.77 (((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (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_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1458])).
% 0.70/0.77 tff(1460,plain,
% 0.70/0.77 (((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (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_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1459, 1457])).
% 0.70/0.77 tff(1461,plain,
% 0.70/0.77 ((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | (big_r(sk7, sk2(sk7)) | big_p(sk9) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_p(sk3(sk9)))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1462,plain,
% 0.70/0.77 ((~![N1: $i, O1: $i, P1: $i] : (big_r(O1, sk2(O1)) | big_p(N1) | (~big_r(O1, P1)) | (~big_p(P1)) | big_p(sk3(N1)))) | big_p(sk9) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk3(sk9))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 0.70/0.77 tff(1463,plain,
% 0.70/0.77 (big_r(sk7, sk2(sk7)) | big_p(sk3(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1462, 1456, 1297, 5, 1255])).
% 0.70/0.77 tff(1464,plain,
% 0.70/0.77 (big_r(sk7, sk2(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1463, 1124])).
% 0.70/0.77 tff(1465,plain,
% 0.70/0.77 ($false),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[295, 265, 1464, 1443, 1412, 1435, 1318, 1125])).
% 0.70/0.77 tff(1466,plain,(big_p(sk3(sk9)) | big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.77 tff(1467,plain,
% 0.70/0.77 (big_p(sk3(sk9))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1466, 5])).
% 0.70/0.77 tff(1468,assumption,(big_p(sk3(sk9))), introduced(assumption)).
% 0.70/0.77 tff(1469,assumption,(big_p(sk8)), introduced(assumption)).
% 0.70/0.77 tff(1470,plain,
% 0.70/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1471,plain,
% 0.70/0.77 (((~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7))) <=> ((~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1472,plain,
% 0.70/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.70/0.77 inference(monotonicity,[status(thm)],[1471])).
% 0.70/0.77 tff(1473,plain,
% 0.70/0.77 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(transitivity,[status(thm)],[1472, 1470])).
% 0.70/0.77 tff(1474,plain,
% 0.70/0.77 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | big_p(sk1(sk7)))),
% 0.70/0.77 inference(quant_inst,[status(thm)],[])).
% 0.70/0.77 tff(1475,plain,
% 0.70/0.77 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.70/0.77 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 0.70/0.77 tff(1476,plain,
% 0.70/0.77 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_p(sk5(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1475, 1089, 1255])).
% 0.70/0.77 tff(1477,plain,
% 0.70/0.77 (big_p(sk5(sk7))),
% 0.70/0.77 inference(unit_resolution,[status(thm)],[1476, 6, 1469])).
% 0.70/0.77 tff(1478,plain,
% 0.70/0.77 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))) <=> ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1479,plain,
% 0.70/0.77 ((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(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.77 inference(rewrite,[status(thm)],[])).
% 0.70/0.77 tff(1480,plain,
% 0.70/0.77 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.70/0.78 inference(monotonicity,[status(thm)],[1479])).
% 0.70/0.78 tff(1481,plain,
% 0.70/0.78 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.78 inference(transitivity,[status(thm)],[1480, 1478])).
% 0.70/0.78 tff(1482,plain,
% 0.70/0.78 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.70/0.78 inference(quant_inst,[status(thm)],[])).
% 0.70/0.78 tff(1483,plain,
% 0.70/0.78 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.70/0.78 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.70/0.78 tff(1484,plain,
% 0.70/0.78 ((~big_p(sk8)) | big_p(sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.70/0.78 inference(unit_resolution,[status(thm)],[1483, 897, 1255])).
% 0.70/0.78 tff(1485,plain,
% 0.70/0.78 (big_r(sk7, sk6(sk7))),
% 0.70/0.78 inference(unit_resolution,[status(thm)],[1484, 6, 1469])).
% 0.70/0.78 tff(1486,plain,
% 0.70/0.78 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.78 inference(rewrite,[status(thm)],[])).
% 0.70/0.78 tff(1487,plain,
% 0.70/0.78 (((~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(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.78 inference(rewrite,[status(thm)],[])).
% 0.70/0.78 tff(1488,plain,
% 0.70/0.78 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8))))),
% 0.70/0.78 inference(monotonicity,[status(thm)],[1487])).
% 0.70/0.78 tff(1489,plain,
% 0.70/0.78 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.70/0.78 inference(transitivity,[status(thm)],[1488, 1486])).
% 0.70/0.78 tff(1490,plain,
% 0.70/0.78 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.70/0.78 inference(quant_inst,[status(thm)],[])).
% 0.70/0.78 tff(1491,plain,
% 0.70/0.78 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~big_p(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 0.76/0.78 tff(1492,plain,
% 0.76/0.78 ((~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1491, 1035, 1255])).
% 0.76/0.78 tff(1493,plain,
% 0.76/0.78 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1492, 6, 1469])).
% 0.76/0.78 tff(1494,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1409, 265, 352, 351, 1493, 1485, 1477, 1468])).
% 0.76/0.78 tff(1495,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,[]))).
% 0.76/0.78 tff(1496,plain,
% 0.76/0.78 (big_p(sk1(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1495, 352, 351, 1468, 1469])).
% 0.76/0.78 tff(1497,plain,
% 0.76/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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_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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1498,plain,
% 0.76/0.78 (((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1499,plain,
% 0.76/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1498])).
% 0.76/0.78 tff(1500,plain,
% 0.76/0.78 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1499, 1497])).
% 0.76/0.78 tff(1501,plain,
% 0.76/0.78 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk8)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1502,plain,
% 0.76/0.78 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.76/0.78 tff(1503,plain,
% 0.76/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1502, 987, 1255])).
% 0.76/0.78 tff(1504,plain,
% 0.76/0.78 (big_r(sk2(sk7), sk1(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1503, 1, 1469])).
% 0.76/0.78 tff(1505,plain,
% 0.76/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1506,plain,
% 0.76/0.78 ((big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8))) <=> (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1507,plain,
% 0.76/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1506])).
% 0.76/0.78 tff(1508,plain,
% 0.76/0.78 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1507, 1505])).
% 0.76/0.78 tff(1509,plain,
% 0.76/0.78 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk7, sk2(sk7)) | big_p(sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1510,plain,
% 0.76/0.78 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.76/0.78 tff(1511,plain,
% 0.76/0.78 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_p(sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1510, 1110, 1255])).
% 0.76/0.78 tff(1512,plain,
% 0.76/0.78 (big_r(sk7, sk2(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1511, 1, 1469])).
% 0.76/0.78 tff(1513,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[444, 265, 1512, 1504, 352, 351, 1496, 1468])).
% 0.76/0.78 tff(1514,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,[]))).
% 0.76/0.78 tff(1515,plain,
% 0.76/0.78 (big_p(sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1514, 1403, 1432, 1467, 1297])).
% 0.76/0.78 tff(1516,plain,
% 0.76/0.78 (big_p(sk1(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1495, 1403, 1432, 1467, 1297])).
% 0.76/0.78 tff(1517,plain,
% 0.76/0.78 (big_p(sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1514, 352, 351, 1468, 1469])).
% 0.76/0.78 tff(1518,plain,
% 0.76/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1519,plain,
% 0.76/0.78 (((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1520,plain,
% 0.76/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1519])).
% 0.76/0.78 tff(1521,plain,
% 0.76/0.78 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1520, 1518])).
% 0.76/0.78 tff(1522,plain,
% 0.76/0.78 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1523,plain,
% 0.76/0.78 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.76/0.78 tff(1524,plain,
% 0.76/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1523, 919, 1255])).
% 0.76/0.78 tff(1525,plain,
% 0.76/0.78 (big_r(sk7, sk6(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1524, 403, 1469])).
% 0.76/0.78 tff(1526,plain,
% 0.76/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1527,plain,
% 0.76/0.78 (((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1528,plain,
% 0.76/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1527])).
% 0.76/0.78 tff(1529,plain,
% 0.76/0.78 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1528, 1526])).
% 0.76/0.78 tff(1530,plain,
% 0.76/0.78 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1531,plain,
% 0.76/0.78 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~big_r(B4, C4)) | (~big_p(C4)) | (~big_p(D4)) | big_r(sk6(B4), sk5(B4)) | big_r(sk2(A4), sk1(A4)) | (~big_r(A4, D4)))) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 0.76/0.78 tff(1532,plain,
% 0.76/0.78 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1531, 1010, 1255])).
% 0.76/0.78 tff(1533,plain,
% 0.76/0.78 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1532, 403, 1469])).
% 0.76/0.78 tff(1534,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1409, 265, 352, 351, 1533, 1525, 1517, 1468])).
% 0.76/0.78 tff(1535,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,[]))).
% 0.76/0.78 tff(1536,plain,
% 0.76/0.78 (big_r(sk2(sk7), sk1(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1535, 1403, 1432, 1467, 1297])).
% 0.76/0.78 tff(1537,plain,
% 0.76/0.78 (~big_r(sk7, sk2(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[444, 265, 1536, 1403, 1432, 1516, 1467])).
% 0.76/0.78 tff(1538,plain,
% 0.76/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1539,plain,
% 0.76/0.78 (((~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_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1540,plain,
% 0.76/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1539])).
% 0.76/0.78 tff(1541,plain,
% 0.76/0.78 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1540, 1538])).
% 0.76/0.78 tff(1542,plain,
% 0.76/0.78 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1543,plain,
% 0.76/0.78 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 0.76/0.78 tff(1544,plain,
% 0.76/0.78 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1543, 940, 1255])).
% 0.76/0.78 tff(1545,plain,
% 0.76/0.78 (big_r(sk7, sk6(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1544, 1537, 1297])).
% 0.76/0.78 tff(1546,plain,
% 0.76/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1547,plain,
% 0.76/0.78 ((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_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1548,plain,
% 0.76/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1547])).
% 0.76/0.78 tff(1549,plain,
% 0.76/0.78 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1548, 1546])).
% 0.76/0.78 tff(1550,plain,
% 0.76/0.78 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk7, sk2(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1551,plain,
% 0.76/0.78 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (big_r(W3, sk2(W3)) | (~big_r(X3, Y3)) | (~big_p(Y3)) | big_r(sk6(X3), sk5(X3)) | (~big_p(Z3)) | (~big_r(W3, Z3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk7, sk8))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.76/0.78 tff(1552,plain,
% 0.76/0.78 (big_r(sk7, sk2(sk7)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1551, 1056, 1255])).
% 0.76/0.78 tff(1553,plain,
% 0.76/0.78 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1552, 1537, 1297])).
% 0.76/0.78 tff(1554,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1409, 265, 1403, 1432, 1553, 1545, 1515, 1467])).
% 0.76/0.78 tff(1555,plain,(big_p(sk9)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.78 tff(1556,plain,
% 0.76/0.78 ((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))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1557,plain,
% 0.76/0.78 (((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))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1558,plain,
% 0.76/0.78 (((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) <=> (big_p(sk8) | (~big_p(sk7)) | big_r(sk9, sk10))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1559,plain,
% 0.76/0.79 ((((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)))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1558])).
% 0.76/0.79 tff(1560,plain,
% 0.76/0.79 ((((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))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1559, 1557])).
% 0.76/0.79 tff(1561,axiom,(((big_p(sk8) | big_r(sk9, sk10)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel38_39')).
% 0.76/0.79 tff(1562,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 0.76/0.79 tff(1563,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1562, 1556])).
% 0.76/0.79 tff(1564,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1563, 1556])).
% 0.76/0.79 tff(1565,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1564, 1556])).
% 0.76/0.79 tff(1566,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1565, 1556])).
% 0.76/0.79 tff(1567,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1566, 1556])).
% 0.76/0.79 tff(1568,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1567, 1556])).
% 0.76/0.79 tff(1569,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1568, 1556])).
% 0.76/0.79 tff(1570,plain,
% 0.76/0.79 (big_p(sk8) | (~big_p(sk9)) | (~big_p(sk7)) | big_r(sk9, sk10)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1569, 1556])).
% 0.76/0.79 tff(1571,plain,
% 0.76/0.79 (big_r(sk9, sk10)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1570, 2, 1555, 1123])).
% 0.76/0.79 tff(1572,plain,
% 0.76/0.79 ((big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1573,plain,
% 0.76/0.79 (((big_p(sk8) | big_p(sk10) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1574,plain,
% 0.76/0.79 (((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk7)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1575,plain,
% 0.76/0.79 ((((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> ((big_p(sk8) | big_p(sk10) | (~big_p(sk7))) | (~big_p(sk9)))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1574])).
% 0.76/0.79 tff(1576,plain,
% 0.76/0.79 ((((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))) <=> (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1575, 1573])).
% 0.76/0.79 tff(1577,axiom,(((big_p(sk10) | big_p(sk8)) | (~big_p(sk7))) | (~big_p(sk9))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel38_38')).
% 0.76/0.79 tff(1578,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.76/0.79 tff(1579,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1578, 1572])).
% 0.76/0.79 tff(1580,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1579, 1572])).
% 0.76/0.79 tff(1581,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1580, 1572])).
% 0.76/0.79 tff(1582,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1581, 1572])).
% 0.76/0.79 tff(1583,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1582, 1572])).
% 0.76/0.79 tff(1584,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1583, 1572])).
% 0.76/0.79 tff(1585,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1584, 1572])).
% 0.76/0.79 tff(1586,plain,
% 0.76/0.79 (big_p(sk8) | big_p(sk10) | (~big_p(sk9)) | (~big_p(sk7))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1585, 1572])).
% 0.76/0.79 tff(1587,plain,
% 0.76/0.79 (big_p(sk10)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1586, 2, 1555, 1123])).
% 0.76/0.79 tff(1588,plain,
% 0.76/0.79 (big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1116, 1110, 1587, 1571])).
% 0.76/0.79 tff(1589,plain,
% 0.76/0.79 (big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1588, 3])).
% 0.76/0.79 tff(1590,plain,
% 0.76/0.79 (big_r(sk9, sk2(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1062, 1056, 1587, 1571])).
% 0.76/0.79 tff(1591,plain,
% 0.76/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1590, 3])).
% 0.76/0.79 tff(1592,plain,
% 0.76/0.79 (big_r(sk9, sk2(sk9)) | big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[946, 940, 1587, 1571])).
% 0.76/0.79 tff(1593,plain,
% 0.76/0.79 (big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1592, 3])).
% 0.76/0.79 tff(1594,plain,
% 0.76/0.79 (((~![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))))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1595,plain,
% 0.76/0.79 ((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))))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1596,plain,
% 0.76/0.79 (((~![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)))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1595])).
% 0.76/0.79 tff(1597,plain,
% 0.76/0.79 (((~![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))))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1596, 1594])).
% 0.76/0.79 tff(1598,plain,
% 0.76/0.79 ((~![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))))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1599,plain,
% 0.76/0.79 ((~![F4: $i, E4: $i] : (big_p(sk8) | (~big_r(F4, E4)) | (~big_p(E4)) | (~big_p(sk7)) | (~big_r(sk9, F4)))) | big_p(sk8) | (~big_p(sk7)) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9)))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.76/0.79 tff(1600,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1599, 2, 1123, 1266, 1593, 1591, 1589])).
% 0.76/0.79 tff(1601,plain,(big_r(sk9, sk2(sk9)) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1602,plain,
% 0.76/0.79 (big_r(sk9, sk2(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1601, 2])).
% 0.76/0.79 tff(1603,plain,
% 0.76/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[993, 987, 1587, 1571])).
% 0.76/0.79 tff(1604,plain,
% 0.76/0.79 (big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1603, 100])).
% 0.76/0.79 tff(1605,plain,
% 0.76/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1016, 1010, 1587, 1571])).
% 0.76/0.79 tff(1606,plain,
% 0.76/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1605, 100])).
% 0.76/0.79 tff(1607,plain,
% 0.76/0.79 (big_r(sk2(sk9), sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[925, 919, 1587, 1571])).
% 0.76/0.79 tff(1608,plain,
% 0.76/0.79 (big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1607, 100])).
% 0.76/0.79 tff(1609,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1599, 2, 1123, 1266, 1608, 1606, 1604])).
% 0.76/0.79 tff(1610,plain,(big_r(sk2(sk9), sk1(sk9)) | big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1611,plain,
% 0.76/0.79 (big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1610, 2])).
% 0.76/0.79 tff(1612,plain,
% 0.76/0.79 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1272, 2, 1123, 1266, 1611])).
% 0.76/0.79 tff(1613,plain,
% 0.76/0.79 (~big_p(sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1612, 1602])).
% 0.76/0.79 tff(1614,plain,
% 0.76/0.79 (big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1095, 1089, 1587, 1571])).
% 0.76/0.79 tff(1615,plain,
% 0.76/0.79 (big_p(sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1614, 1613])).
% 0.76/0.79 tff(1616,plain,
% 0.76/0.79 (big_r(sk6(sk9), sk5(sk9)) | big_p(sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1041, 1035, 1587, 1571])).
% 0.76/0.79 tff(1617,plain,
% 0.76/0.79 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1616, 1613])).
% 0.76/0.79 tff(1618,plain,
% 0.76/0.79 (big_p(sk1(sk9)) | big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[903, 897, 1587, 1571])).
% 0.76/0.79 tff(1619,plain,
% 0.76/0.79 (big_r(sk9, sk6(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1618, 1613])).
% 0.76/0.79 tff(1620,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1599, 2, 1123, 1266, 1619, 1617, 1615])).
% 0.76/0.79 tff(1621,plain,(big_p(sk8)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1622,plain,
% 0.76/0.79 (big_p(sk1(sk7)) | big_p(sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1476, 1621])).
% 0.76/0.79 tff(1623,plain,
% 0.76/0.79 (big_p(sk1(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1622, 1])).
% 0.76/0.79 tff(1624,plain,
% 0.76/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_p(sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1503, 1621])).
% 0.76/0.79 tff(1625,plain,
% 0.76/0.79 (big_r(sk2(sk7), sk1(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1624, 1])).
% 0.76/0.79 tff(1626,plain,
% 0.76/0.79 (big_r(sk7, sk2(sk7)) | big_p(sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1511, 1621])).
% 0.76/0.79 tff(1627,plain,
% 0.76/0.79 (big_r(sk7, sk2(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1626, 1])).
% 0.76/0.79 tff(1628,plain,
% 0.76/0.79 (big_p(sk10)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[529, 1555, 513, 1627, 1625, 1623])).
% 0.76/0.79 tff(1629,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[476, 1555, 457, 470, 1627, 1625, 1623])).
% 0.76/0.79 tff(1630,plain,(big_p(sk5(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1631,plain,
% 0.76/0.79 (big_p(sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1630, 457])).
% 0.76/0.79 tff(1632,plain,
% 0.76/0.79 (big_p(sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1484, 1621])).
% 0.76/0.79 tff(1633,plain,
% 0.76/0.79 (big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1632, 6])).
% 0.76/0.79 tff(1634,plain,
% 0.76/0.79 (big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1492, 1621])).
% 0.76/0.79 tff(1635,plain,
% 0.76/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1634, 6])).
% 0.76/0.79 tff(1636,plain,
% 0.76/0.79 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1637,plain,
% 0.76/0.79 (((~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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1638,plain,
% 0.76/0.79 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1637])).
% 0.76/0.79 tff(1639,plain,
% 0.76/0.79 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1638, 1636])).
% 0.76/0.79 tff(1640,plain,
% 0.76/0.79 ((~![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))))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1641,plain,
% 0.76/0.79 ((~![L4: $i, K4: $i] : ((~big_p(sk9)) | (~big_r(L4, K4)) | (~big_p(K4)) | big_r(sk9, sk10) | (~big_r(sk7, L4)))) | (~big_p(sk9)) | big_r(sk9, sk10) | (~big_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 0.76/0.79 tff(1642,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1641, 1555, 457, 470, 1635, 1633, 1631])).
% 0.76/0.79 tff(1643,plain,(big_p(sk1(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1644,plain,
% 0.76/0.79 (big_p(sk1(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1643, 457])).
% 0.76/0.79 tff(1645,plain,
% 0.76/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1524, 1621])).
% 0.76/0.79 tff(1646,plain,
% 0.76/0.79 (big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1645, 403])).
% 0.76/0.79 tff(1647,plain,
% 0.76/0.79 (big_r(sk2(sk7), sk1(sk7)) | big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1532, 1621])).
% 0.76/0.79 tff(1648,plain,
% 0.76/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1647, 403])).
% 0.76/0.79 tff(1649,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1641, 1555, 457, 470, 1648, 1646, 1631])).
% 0.76/0.79 tff(1650,plain,(big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1651,plain,
% 0.76/0.79 (big_r(sk2(sk7), sk1(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1650, 457])).
% 0.76/0.79 tff(1652,plain,
% 0.76/0.79 ((~big_p(sk1(sk7))) | (~big_r(sk7, sk2(sk7)))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[476, 1555, 457, 470, 1651])).
% 0.76/0.79 tff(1653,plain,
% 0.76/0.79 (~big_r(sk7, sk2(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1652, 1644])).
% 0.76/0.79 tff(1654,plain,
% 0.76/0.79 (big_r(sk7, sk2(sk7)) | big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1544, 1621])).
% 0.76/0.79 tff(1655,plain,
% 0.76/0.79 (big_r(sk7, sk6(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1654, 1653])).
% 0.76/0.79 tff(1656,plain,
% 0.76/0.79 (big_r(sk7, sk2(sk7)) | big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1552, 1621])).
% 0.76/0.79 tff(1657,plain,
% 0.76/0.79 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1656, 1653])).
% 0.76/0.79 tff(1658,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1641, 1555, 457, 470, 1657, 1655, 1631])).
% 0.76/0.79 tff(1659,plain,(big_r(sk9, sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1660,plain,
% 0.76/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1661,plain,
% 0.76/0.79 (((~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9))) <=> ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1662,plain,
% 0.76/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1661])).
% 0.76/0.79 tff(1663,plain,
% 0.76/0.79 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1662, 1660])).
% 0.76/0.79 tff(1664,plain,
% 0.76/0.79 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk8)) | (~big_p(sk10)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9)))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1665,plain,
% 0.76/0.79 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 0.76/0.79 tff(1666,plain,
% 0.76/0.79 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_p(sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1665, 1089, 1621, 1659, 1255])).
% 0.76/0.79 tff(1667,plain,
% 0.76/0.79 (big_p(sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1666, 1628, 1])).
% 0.76/0.79 tff(1668,plain,
% 0.76/0.79 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1669,plain,
% 0.76/0.79 (((~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(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1670,plain,
% 0.76/0.79 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1669])).
% 0.76/0.79 tff(1671,plain,
% 0.76/0.79 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1670, 1668])).
% 0.76/0.79 tff(1672,plain,
% 0.76/0.79 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1673,plain,
% 0.76/0.79 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 0.76/0.79 tff(1674,plain,
% 0.76/0.79 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1673, 987, 1621, 1659, 1255])).
% 0.76/0.79 tff(1675,plain,
% 0.76/0.79 (big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1674, 1628, 1])).
% 0.76/0.79 tff(1676,plain,
% 0.76/0.79 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (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(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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1677,plain,
% 0.76/0.79 ((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(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1678,plain,
% 0.76/0.79 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1677])).
% 0.76/0.79 tff(1679,plain,
% 0.76/0.79 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1678, 1676])).
% 0.76/0.79 tff(1680,plain,
% 0.76/0.79 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk9, sk2(sk9)) | big_p(sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1681,plain,
% 0.76/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 0.76/0.80 tff(1682,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_p(sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1681, 1110, 1621, 1659, 1255])).
% 0.76/0.80 tff(1683,plain,
% 0.76/0.80 (big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1682, 1628, 1])).
% 0.76/0.80 tff(1684,plain,
% 0.76/0.80 ($false),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[295, 265, 1627, 1625, 1683, 1675, 1623, 1667])).
% 0.76/0.80 tff(1685,plain,(big_p(sk5(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.80 tff(1686,plain,
% 0.76/0.80 (((~![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(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1687,plain,
% 0.76/0.80 ((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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1688,plain,
% 0.76/0.80 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1687])).
% 0.76/0.80 tff(1689,plain,
% 0.76/0.80 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1688, 1686])).
% 0.76/0.80 tff(1690,plain,
% 0.76/0.80 ((~![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))))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1691,plain,
% 0.76/0.80 ((~![J4: $i, I4: $i] : (big_p(sk10) | (~big_p(sk9)) | (~big_r(J4, I4)) | (~big_p(I4)) | (~big_r(sk7, J4)))) | big_p(sk10) | (~big_p(sk9)) | (~big_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.76/0.80 tff(1692,plain,
% 0.76/0.80 ($false),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1691, 502, 1555, 513, 1635, 1633, 1685])).
% 0.76/0.80 tff(1693,plain,(big_p(sk1(sk7)) | big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.80 tff(1694,plain,
% 0.76/0.80 (big_p(sk1(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1693, 502])).
% 0.76/0.80 tff(1695,plain,
% 0.76/0.80 ($false),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1691, 502, 1555, 513, 1648, 1646, 1685])).
% 0.76/0.80 tff(1696,plain,(big_r(sk2(sk7), sk1(sk7)) | big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.80 tff(1697,plain,
% 0.76/0.80 (big_r(sk2(sk7), sk1(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1696, 502])).
% 0.76/0.80 tff(1698,plain,
% 0.76/0.80 (~big_r(sk7, sk2(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[529, 502, 1555, 513, 1697, 1694])).
% 0.76/0.80 tff(1699,plain,
% 0.76/0.80 (big_r(sk7, sk6(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1654, 1698])).
% 0.76/0.80 tff(1700,plain,
% 0.76/0.80 (big_r(sk6(sk7), sk5(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1656, 1698])).
% 0.76/0.80 tff(1701,plain,
% 0.76/0.80 ($false),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1691, 502, 1555, 513, 1700, 1699, 1685])).
% 0.76/0.80 tff(1702,plain,(big_p(sk10)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.80 tff(1703,plain,
% 0.76/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1704,plain,
% 0.76/0.80 ((big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10))) <=> (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1705,plain,
% 0.76/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1704])).
% 0.76/0.80 tff(1706,plain,
% 0.76/0.80 (((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (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_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1705, 1703])).
% 0.76/0.80 tff(1707,plain,
% 0.76/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | (big_r(sk7, sk2(sk7)) | big_p(sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1708,plain,
% 0.76/0.80 ((~![A3: $i, Y2: $i, B3: $i, Z2: $i] : (big_r(Z2, sk2(Z2)) | big_p(sk5(Y2)) | (~big_p(B3)) | (~big_r(Z2, B3)) | (~big_r(Y2, A3)) | (~big_p(A3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 0.76/0.80 tff(1709,plain,
% 0.76/0.80 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1708, 1110, 1621, 1659, 1255])).
% 0.76/0.80 tff(1710,plain,
% 0.76/0.80 (big_p(sk5(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1709, 211, 1702])).
% 0.76/0.80 tff(1711,assumption,(~big_r(sk7, sk6(sk7))), introduced(assumption)).
% 0.76/0.80 tff(1712,plain,
% 0.76/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1713,plain,
% 0.76/0.80 ((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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1714,plain,
% 0.76/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1713])).
% 0.76/0.80 tff(1715,plain,
% 0.76/0.80 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1714, 1712])).
% 0.76/0.80 tff(1716,plain,
% 0.76/0.80 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk9)) | (~big_p(sk10)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1717,plain,
% 0.76/0.80 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 0.76/0.80 tff(1718,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_p(sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1717, 897, 1621, 1659, 1255])).
% 0.76/0.80 tff(1719,plain,
% 0.76/0.80 (big_p(sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1718, 1711, 1702])).
% 0.76/0.80 tff(1720,plain,
% 0.76/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1721,plain,
% 0.76/0.80 (((~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7))) <=> ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1722,plain,
% 0.76/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1721])).
% 0.76/0.80 tff(1723,plain,
% 0.76/0.80 (((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~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(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1722, 1720])).
% 0.76/0.80 tff(1724,plain,
% 0.76/0.80 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | ((~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)) | big_p(sk1(sk7)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1725,plain,
% 0.76/0.80 ((~![U2: $i, W2: $i, X2: $i, V2: $i] : ((~big_p(W2)) | (~big_p(X2)) | (~big_r(V2, W2)) | (~big_r(U2, X2)) | big_p(sk5(V2)) | big_p(sk1(U2)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 0.76/0.80 tff(1726,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_p(sk5(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1725, 1089, 1621, 1659, 1255])).
% 0.76/0.80 tff(1727,plain,
% 0.76/0.80 (big_p(sk5(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1726, 6, 1702])).
% 0.76/0.80 tff(1728,assumption,(~big_r(sk6(sk7), sk5(sk7))), introduced(assumption)).
% 0.76/0.80 tff(1729,plain,
% 0.76/0.80 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1730,plain,
% 0.76/0.80 (((~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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1731,plain,
% 0.76/0.80 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1730])).
% 0.76/0.80 tff(1732,plain,
% 0.76/0.80 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1731, 1729])).
% 0.76/0.80 tff(1733,plain,
% 0.76/0.80 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk10)) | big_p(sk1(sk9)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | (~big_r(sk7, sk8)) | big_r(sk6(sk7), sk5(sk7)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1734,plain,
% 0.76/0.80 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk1(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 0.76/0.80 tff(1735,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_p(sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1734, 1035, 1621, 1659, 1255])).
% 0.76/0.80 tff(1736,plain,
% 0.76/0.80 (big_p(sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1735, 1728, 1702])).
% 0.76/0.80 tff(1737,plain,
% 0.76/0.80 (big_p(sk1(sk7))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1634, 1728])).
% 0.76/0.80 tff(1738,plain,
% 0.76/0.80 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1739,plain,
% 0.76/0.80 (((~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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1740,plain,
% 0.76/0.80 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1739])).
% 0.76/0.80 tff(1741,plain,
% 0.76/0.80 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1740, 1738])).
% 0.76/0.80 tff(1742,plain,
% 0.76/0.80 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk7, sk8)) | (~big_p(sk8)) | (~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9)) | (~big_r(sk9, sk10)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1743,plain,
% 0.76/0.80 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 0.76/0.80 tff(1744,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1743, 1010, 1621, 1659, 1255])).
% 0.76/0.80 tff(1745,plain,
% 0.76/0.80 (big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1744, 1728, 1702])).
% 0.76/0.80 tff(1746,plain,
% 0.76/0.80 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1747,plain,
% 0.76/0.80 ((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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1748,plain,
% 0.76/0.80 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1747])).
% 0.76/0.80 tff(1749,plain,
% 0.76/0.80 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1748, 1746])).
% 0.76/0.80 tff(1750,plain,
% 0.76/0.80 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1751,plain,
% 0.76/0.80 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk10)) | (~big_p(sk8)) | big_r(sk6(sk7), sk5(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 0.76/0.80 tff(1752,plain,
% 0.76/0.80 ((~big_p(sk10)) | big_r(sk6(sk7), sk5(sk7)) | big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1751, 1056, 1621, 1659, 1255])).
% 0.76/0.80 tff(1753,plain,
% 0.76/0.80 (big_r(sk9, sk2(sk9))),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1752, 1728, 1702])).
% 0.76/0.80 tff(1754,plain,
% 0.76/0.80 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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_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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1755,plain,
% 0.76/0.80 (((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1756,plain,
% 0.76/0.81 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1755])).
% 0.76/0.81 tff(1757,plain,
% 0.76/0.81 (((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(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(N3)) | (~big_p(M3)) | (~big_r(K3, M3)) | big_p(sk5(K3)) | (~big_r(L3, N3)) | big_r(sk2(L3), sk1(L3)))) | big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1756, 1754])).
% 0.76/0.81 tff(1758,plain,
% 0.76/0.81 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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(sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_p(sk5(sk9)) | (~big_r(sk7, sk8)) | big_r(sk2(sk7), sk1(sk7)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1759,plain,
% 0.76/0.81 ((~![L3: $i, N3: $i, M3: $i, K3: $i] : ((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_p(sk5(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 0.76/0.81 tff(1760,plain,
% 0.76/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_p(sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1759, 987, 1621, 1659, 1255])).
% 0.76/0.81 tff(1761,plain,
% 0.76/0.81 (big_p(sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1760, 403, 1702])).
% 0.76/0.81 tff(1762,plain,
% 0.76/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1763,plain,
% 0.76/0.81 (((~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_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)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1764,plain,
% 0.76/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1763])).
% 0.76/0.81 tff(1765,plain,
% 0.76/0.81 (((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(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_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(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1764, 1762])).
% 0.76/0.81 tff(1766,plain,
% 0.76/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk9, sk10)) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk6(sk9), sk5(sk9)) | big_r(sk2(sk7), sk1(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1767,plain,
% 0.76/0.81 ((~![A4: $i, C4: $i, B4: $i, D4: $i] : ((~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(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.76/0.81 tff(1768,plain,
% 0.76/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1767, 1010, 1621, 1659, 1255])).
% 0.76/0.81 tff(1769,plain,
% 0.76/0.81 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1768, 403, 1702])).
% 0.76/0.81 tff(1770,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1771,plain,
% 0.76/0.81 (((~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_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1772,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1771])).
% 0.76/0.81 tff(1773,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1772, 1770])).
% 0.76/0.81 tff(1774,plain,
% 0.76/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk10)) | (~big_r(sk7, sk8)) | (~big_p(sk8)) | big_r(sk2(sk7), sk1(sk7)) | big_r(sk9, sk6(sk9)) | (~big_r(sk9, sk10)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1775,plain,
% 0.76/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 0.76/0.81 tff(1776,plain,
% 0.76/0.81 (big_r(sk2(sk7), sk1(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1775, 919, 1621, 1659, 1255])).
% 0.76/0.81 tff(1777,plain,
% 0.76/0.81 (big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1776, 403, 1702])).
% 0.76/0.81 tff(1778,plain,
% 0.76/0.81 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1779,plain,
% 0.76/0.81 (((~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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1780,plain,
% 0.76/0.81 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1779])).
% 0.76/0.81 tff(1781,plain,
% 0.76/0.81 (((~![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_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7))))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1780, 1778])).
% 0.76/0.81 tff(1782,plain,
% 0.76/0.81 ((~![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))))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1783,plain,
% 0.76/0.81 ((~![N4: $i, O4: $i, P4: $i, M4: $i] : ((~big_p(M4)) | (~big_r(O4, M4)) | (~big_p(N4)) | (~big_r(P4, N4)) | (~big_r(sk7, P4)) | (~big_r(sk9, O4)))) | (~big_r(sk6(sk9), sk5(sk9))) | (~big_p(sk5(sk9))) | (~big_r(sk9, sk6(sk9))) | (~big_r(sk7, sk6(sk7))) | (~big_p(sk5(sk7))) | (~big_r(sk6(sk7), sk5(sk7)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.76/0.81 tff(1784,plain,
% 0.76/0.81 ($false),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1783, 265, 1777, 1769, 1648, 1646, 1685, 1761])).
% 0.76/0.81 tff(1785,plain,(big_r(sk2(sk7), sk1(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.81 tff(1786,plain,
% 0.76/0.81 (big_r(sk7, sk2(sk7))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1656, 1728])).
% 0.76/0.81 tff(1787,plain,
% 0.76/0.81 ($false),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[295, 265, 1786, 1785, 1753, 1745, 1737, 1736])).
% 0.76/0.81 tff(1788,plain,(big_r(sk6(sk7), sk5(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.81 tff(1789,plain,
% 0.76/0.81 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1790,plain,
% 0.76/0.81 (((~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(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1791,plain,
% 0.76/0.81 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1790])).
% 0.76/0.81 tff(1792,plain,
% 0.76/0.81 (((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(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(V3)) | big_p(sk1(S3)) | (~big_r(S3, V3)) | (~big_p(U3)) | (~big_r(T3, U3)) | big_r(sk6(T3), sk5(T3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1791, 1789])).
% 0.76/0.81 tff(1793,plain,
% 0.76/0.81 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk8)) | big_p(sk1(sk7)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1794,plain,
% 0.76/0.81 ((~![T3: $i, S3: $i, U3: $i, V3: $i] : ((~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(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 0.76/0.81 tff(1795,plain,
% 0.76/0.81 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1794, 1035, 1621, 1659, 1255])).
% 0.76/0.81 tff(1796,plain,
% 0.76/0.81 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1795, 6, 1702])).
% 0.76/0.81 tff(1797,plain,
% 0.76/0.81 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1798,plain,
% 0.76/0.81 ((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(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1799,plain,
% 0.76/0.81 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1798])).
% 0.76/0.81 tff(1800,plain,
% 0.76/0.81 (((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(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(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1799, 1797])).
% 0.76/0.81 tff(1801,plain,
% 0.76/0.81 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (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(sk7)) | (~big_p(sk8)) | big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | (~big_r(sk9, sk10)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1802,plain,
% 0.76/0.81 ((~![E3: $i, F3: $i, D3: $i, C3: $i] : (big_p(sk1(C3)) | (~big_p(F3)) | big_r(D3, sk6(D3)) | (~big_r(C3, F3)) | (~big_p(E3)) | (~big_r(D3, E3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_p(sk1(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.76/0.81 tff(1803,plain,
% 0.76/0.81 ((~big_p(sk10)) | big_p(sk1(sk7)) | big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1802, 897, 1621, 1659, 1255])).
% 0.76/0.81 tff(1804,plain,
% 0.76/0.81 (big_r(sk9, sk6(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1803, 6, 1702])).
% 0.76/0.81 tff(1805,plain,
% 0.76/0.81 ($false),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1783, 265, 1804, 1796, 1788, 1633, 1685, 1727])).
% 0.76/0.81 tff(1806,plain,(big_p(sk1(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.81 tff(1807,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1808,plain,
% 0.76/0.81 (((~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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1809,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1808])).
% 0.76/0.81 tff(1810,plain,
% 0.76/0.81 (((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(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(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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1809, 1807])).
% 0.76/0.81 tff(1811,plain,
% 0.76/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk8)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk7, sk6(sk7)) | (~big_r(sk7, sk8)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1812,plain,
% 0.76/0.81 ((~![O3: $i, P3: $i, R3: $i, Q3: $i] : ((~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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 0.76/0.81 tff(1813,plain,
% 0.76/0.81 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1812, 919, 1621, 1659, 1255])).
% 0.76/0.81 tff(1814,plain,
% 0.76/0.81 (big_r(sk2(sk9), sk1(sk9))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1813, 1711, 1702])).
% 0.76/0.81 tff(1815,plain,
% 0.76/0.81 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1816,plain,
% 0.76/0.81 (((~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(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1817,plain,
% 0.76/0.81 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | ((~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1816])).
% 0.76/0.81 tff(1818,plain,
% 0.76/0.81 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1817, 1815])).
% 0.76/0.81 tff(1819,plain,
% 0.76/0.81 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(sk10)) | (~big_r(sk9, sk10)) | (~big_p(sk8)) | big_r(sk9, sk2(sk9)) | (~big_r(sk7, sk8)) | big_r(sk7, sk6(sk7)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1820,plain,
% 0.76/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (~big_p(sk10)) | (~big_p(sk8)) | big_r(sk7, sk6(sk7)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk2(sk9))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 0.76/0.82 tff(1821,plain,
% 0.76/0.82 ((~big_p(sk10)) | big_r(sk7, sk6(sk7)) | big_r(sk9, sk2(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1820, 940, 1621, 1659, 1255])).
% 0.76/0.82 tff(1822,plain,
% 0.76/0.82 (big_r(sk9, sk2(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1821, 1711, 1702])).
% 0.76/0.82 tff(1823,plain,
% 0.76/0.82 (big_r(sk7, sk2(sk7))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1654, 1711])).
% 0.76/0.82 tff(1824,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[295, 265, 1823, 1785, 1822, 1814, 1806, 1719])).
% 0.76/0.82 tff(1825,plain,(big_r(sk7, sk6(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1826,plain,
% 0.76/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1827,plain,
% 0.76/0.82 ((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_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1828,plain,
% 0.76/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1827])).
% 0.76/0.82 tff(1829,plain,
% 0.76/0.82 (((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(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_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(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1828, 1826])).
% 0.76/0.82 tff(1830,plain,
% 0.76/0.82 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9)) | (~big_p(sk8)) | (~big_r(sk7, sk8)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1831,plain,
% 0.76/0.82 ((~![Z3: $i, Y3: $i, X3: $i, W3: $i] : (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(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 0.76/0.82 tff(1832,plain,
% 0.76/0.82 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1831, 1056, 1621, 1659, 1255])).
% 0.76/0.82 tff(1833,plain,
% 0.76/0.82 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1832, 211, 1702])).
% 0.76/0.82 tff(1834,plain,
% 0.76/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1835,plain,
% 0.76/0.82 (((~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_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1836,plain,
% 0.76/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1835])).
% 0.76/0.82 tff(1837,plain,
% 0.76/0.82 (((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(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(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1836, 1834])).
% 0.76/0.82 tff(1838,plain,
% 0.76/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~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(sk8)) | (~big_r(sk7, sk8)) | (~big_p(sk10)) | big_r(sk7, sk2(sk7)) | (~big_r(sk9, sk10)) | big_r(sk9, sk6(sk9)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1839,plain,
% 0.76/0.82 ((~![G3: $i, H3: $i, I3: $i, J3: $i] : ((~big_p(J3)) | (~big_r(H3, J3)) | (~big_p(I3)) | big_r(H3, sk2(H3)) | (~big_r(G3, I3)) | big_r(G3, sk6(G3)))) | big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | (~big_p(sk8)) | (~big_r(sk9, sk10)) | (~big_r(sk7, sk8)) | big_r(sk9, sk6(sk9))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 0.76/0.82 tff(1840,plain,
% 0.76/0.82 (big_r(sk7, sk2(sk7)) | (~big_p(sk10)) | big_r(sk9, sk6(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1839, 940, 1621, 1659, 1255])).
% 0.76/0.82 tff(1841,plain,
% 0.76/0.82 (big_r(sk9, sk6(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1840, 211, 1702])).
% 0.76/0.82 tff(1842,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1783, 265, 1841, 1833, 1788, 1825, 1685, 1710])).
% 0.76/0.82 tff(1843,plain,(big_r(sk7, sk2(sk7))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1844,plain,
% 0.76/0.82 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_p(sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[993, 987, 1659])).
% 0.76/0.82 tff(1845,plain,
% 0.76/0.82 (big_p(sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1844, 100, 1702])).
% 0.76/0.82 tff(1846,plain,
% 0.76/0.82 ((~big_p(sk10)) | big_r(sk2(sk9), sk1(sk9)) | big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1016, 1010, 1659])).
% 0.76/0.82 tff(1847,plain,
% 0.76/0.82 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1846, 100, 1702])).
% 0.76/0.82 tff(1848,plain,
% 0.76/0.82 (big_r(sk9, sk6(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_p(sk1(sk7))) | (~big_p(sk10))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[952, 1659])).
% 0.76/0.82 tff(1849,plain,
% 0.76/0.82 (big_r(sk9, sk6(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1848, 1843, 1702, 1785, 1806])).
% 0.76/0.82 tff(1850,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1075, 265, 1843, 1785, 1806, 1849, 1847, 1845])).
% 0.76/0.82 tff(1851,plain,(big_r(sk2(sk9), sk1(sk9))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1852,plain,
% 0.76/0.82 (big_r(sk6(sk9), sk5(sk9)) | (~big_r(sk7, sk2(sk7))) | (~big_r(sk2(sk7), sk1(sk7))) | (~big_r(sk2(sk9), sk1(sk9))) | (~big_p(sk1(sk7))) | (~big_p(sk10))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1068, 1659])).
% 0.76/0.82 tff(1853,plain,
% 0.76/0.82 (big_r(sk6(sk9), sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1852, 1851, 1785, 1806, 1702, 1843])).
% 0.76/0.82 tff(1854,plain,
% 0.76/0.82 (~big_p(sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1075, 265, 1843, 1785, 1806, 1849, 1853])).
% 0.76/0.82 tff(1855,plain,
% 0.76/0.82 ((~big_p(sk10)) | big_r(sk9, sk2(sk9)) | big_p(sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1116, 1110, 1659])).
% 0.76/0.82 tff(1856,plain,
% 0.76/0.82 (big_r(sk9, sk2(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1855, 1854, 1702])).
% 0.76/0.82 tff(1857,plain,
% 0.76/0.82 ((~big_p(sk10)) | big_p(sk1(sk9)) | big_p(sk5(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1095, 1089, 1659])).
% 0.76/0.82 tff(1858,plain,
% 0.76/0.82 (big_p(sk1(sk9))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1857, 1854, 1702])).
% 0.76/0.82 tff(1859,plain,
% 0.76/0.82 ((~big_r(sk9, sk2(sk9))) | (~big_p(sk1(sk9)))),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[295, 265, 1843, 1785, 1851, 1806])).
% 0.76/0.82 tff(1860,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1859, 1858, 1856])).
% 0.76/0.82 % SZS output end Proof
%------------------------------------------------------------------------------